Practice sheet

Fresh questions from the whole chapter, to do on paper.

New questions Include answers

To save a PDF, choose “Save as PDF” in the print dialog.

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

$33$
$76$
$13$
$138$
$9$
$5$
$1800$
$120$
$6$
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)