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$\triangle ABC \cong \triangle DEF$ with $AB = 3$ , $BC = 11$ and $CA = 18$ . Find $DE$ .
$\triangle PQR \cong \triangle XYZ$ , with $\angle Q = 43^\circ$ and $\angle R = 40^\circ$ . Find $\angle X$ , in degrees.
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 5)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 7)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 2)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 3)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 6)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 8)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 4)?
1. $TU$
2. $ST$
3. $SU$
$\triangle KLM \cong \triangle STU$ . Which segment corresponds to $LM$ (length 9)?
1. $TU$
2. $ST$
3. $SU$
Two triangles have two pairs of equal sides (3 cm and 5 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two pairs of equal sides (9 cm and 11 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two pairs of equal sides (5 cm and 7 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two pairs of equal sides (4 cm and 6 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two pairs of equal sides (6 cm and 8 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two pairs of equal sides (8 cm and 10 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two pairs of equal sides (7 cm and 9 cm) and the angles between those sides equal. Which criterion shows they are congruent?
1. SAS
2. SSA
3. AAA
Two triangles have two equal pairs of sides (3 and 6) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles have two equal pairs of sides (5 and 8) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles have two equal pairs of sides (8 and 11) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles have two equal pairs of sides (9 and 12) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles have two equal pairs of sides (4 and 7) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles have two equal pairs of sides (6 and 9) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles have two equal pairs of sides (7 and 10) and an equal angle not between them. Must they be congruent?
1. Not necessarily: side-side-angle can give two different triangles
2. Yes, by SSA
3. Yes, by SAS
Two triangles both have angles $48^\circ$ , $60^\circ$ and $72^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $37^\circ$ , $60^\circ$ and $83^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $55^\circ$ , $60^\circ$ and $65^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $44^\circ$ , $60^\circ$ and $76^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $46^\circ$ , $60^\circ$ and $74^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $34^\circ$ , $60^\circ$ and $86^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $42^\circ$ , $60^\circ$ and $78^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $60^\circ$ , $60^\circ$ and $60^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $54^\circ$ , $60^\circ$ and $66^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $40^\circ$ , $60^\circ$ and $80^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $31^\circ$ , $60^\circ$ and $89^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $68^\circ$ , $60^\circ$ and $52^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $65^\circ$ , $60^\circ$ and $55^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $32^\circ$ , $60^\circ$ and $88^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $47^\circ$ , $60^\circ$ and $73^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $67^\circ$ , $60^\circ$ and $53^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $39^\circ$ , $60^\circ$ and $81^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $64^\circ$ , $60^\circ$ and $56^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $49^\circ$ , $60^\circ$ and $71^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $57^\circ$ , $60^\circ$ and $63^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $56^\circ$ , $60^\circ$ and $64^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $43^\circ$ , $60^\circ$ and $77^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $50^\circ$ , $60^\circ$ and $70^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $66^\circ$ , $60^\circ$ and $54^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $53^\circ$ , $60^\circ$ and $67^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $63^\circ$ , $60^\circ$ and $57^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $30^\circ$ , $60^\circ$ and $90^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $33^\circ$ , $60^\circ$ and $87^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $70^\circ$ , $60^\circ$ and $50^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $69^\circ$ , $60^\circ$ and $51^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $36^\circ$ , $60^\circ$ and $84^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $62^\circ$ , $60^\circ$ and $58^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $51^\circ$ , $60^\circ$ and $69^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $35^\circ$ , $60^\circ$ and $85^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $41^\circ$ , $60^\circ$ and $79^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $58^\circ$ , $60^\circ$ and $62^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $61^\circ$ , $60^\circ$ and $59^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $59^\circ$ , $60^\circ$ and $61^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $45^\circ$ , $60^\circ$ and $75^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $38^\circ$ , $60^\circ$ and $82^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
Two triangles both have angles $52^\circ$ , $60^\circ$ and $68^\circ$ . Are they congruent?
1. Not necessarily: they have the same shape but may differ in size
2. Yes, all three angles match
3. No, never
An isosceles triangle has apex angle $114^\circ$ (between the two equal sides). Find each base angle, in degrees.
Each base angle of an isosceles triangle measures $52^\circ$ . Find the apex angle, in degrees.
Point $P$ lies on the perpendicular bisector of $AB$ , and $PA = 13$ . Find $PB$ .Not to scale
In parallelogram $ABCD$ , $\angle A = 42^\circ$ . Find $\angle B$ , in degrees.
The diagonals of parallelogram $ABCD$ meet at $M$ , and $AC = 18$ . Find $AM$ .Not to scale
In parallelogram $ABCD$ , $AB = 2x + 3$ and $CD = x + 8$ . Find $x$ .Not to scale
What is the sum of the interior angles of a polygon with 12 sides, in degrees?
Each exterior angle of a regular polygon with 3 sides measures how many degrees?Not to scale
The interior angles of a polygon add up to 720°. How many sides does the polygon have?
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 6 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 3 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 9 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 4 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 5 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 7 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
Segments $AD$ and $BC$ cross at their common midpoint $M$ (so $AM = MD$ and $BM = MC$ , each pair 8 cm). Put the steps proving $\triangle AMB \cong \triangle DMC$ in order.Not to scale
- $AM = MD$ and $BM = MC$ (M is the midpoint)
- $\angle AMB = \angle DMC$ (vertical angles)
- Two sides and the included angle match: SAS
- So $\triangle AMB \cong \triangle DMC$
In a proof, two segments of length 3 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
In a proof, two segments of length 6 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
In a proof, two segments of length 9 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
In a proof, two segments of length 8 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
In a proof, two segments of length 4 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
In a proof, two segments of length 7 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
In a proof, two segments of length 5 cross at $M$ . Which reason justifies $\angle AMB = \angle DMC$ ?Not to scale
1. Vertical angles are equal
2. Corresponding angles of parallel lines
3. Corresponding parts of congruent triangles
Two triangles have two equal angles ( $54^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $47^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $64^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $69^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $70^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $35^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $60^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $31^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $30^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $65^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $39^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $55^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $61^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $59^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $40^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $37^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $49^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $36^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $34^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $52^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $38^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $41^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $53^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $68^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $48^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $57^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $50^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $42^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $51^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $45^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $32^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $43^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $63^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $62^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $33^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $58^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $56^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $44^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $46^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $67^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent
Two triangles have two equal angles ( $66^\circ$ and $70^\circ$ ) and an equal side that is not between them. Which criterion applies?
1. AAS (equivalent to ASA, since the third angles are equal too)
2. SSA
3. None: they need not be congruent

Answers

$3$
$97$
$TU$
SAS
Not necessarily: side-side-angle can give two different triangles
Not necessarily: they have the same shape but may differ in size
$33$
$76$
$13$
$138$
$9$
$5$
$1800$
$120$
$6$
1. $AM = MD$ and $BM = MC$ (M is the midpoint) 2. $\angle AMB = \angle DMC$ (vertical angles) 3. Two sides and the included angle match: SAS 4. So $\triangle AMB \cong \triangle DMC$
Vertical angles are equal
AAS (equivalent to ASA, since the third angles are equal too)