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Put the steps for constructing the perpendicular bisector of a segment AB of length 7 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
Put the steps for constructing the perpendicular bisector of a segment AB of length 9 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
Put the steps for constructing the perpendicular bisector of a segment AB of length 6 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
Put the steps for constructing the perpendicular bisector of a segment AB of length 4 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
Put the steps for constructing the perpendicular bisector of a segment AB of length 10 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
Put the steps for constructing the perpendicular bisector of a segment AB of length 5 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
Put the steps for constructing the perpendicular bisector of a segment AB of length 8 cm in order.
- With the compass point on A, draw an arc with a radius of more than half of AB
- Keep the same opening; with the point on B, draw an arc that crosses the first one twice
- Label the two crossing points P and Q
- Draw the line through P and Q with the straightedge
In the construction of the perpendicular bisector of AB (AB = 10 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 10 cm
In the construction of the perpendicular bisector of AB (AB = 7 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 7 cm
In the construction of the perpendicular bisector of AB (AB = 5 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 5 cm
In the construction of the perpendicular bisector of AB (AB = 4 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 4 cm
In the construction of the perpendicular bisector of AB (AB = 6 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 6 cm
In the construction of the perpendicular bisector of AB (AB = 9 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 9 cm
In the construction of the perpendicular bisector of AB (AB = 8 cm), why does the line PQ through the two arc crossings bisect AB at a right angle?
1. P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
2. Because the angle measures 90° with a protractor
3. Because the arcs have a radius of 8 cm
To inscribe a regular hexagon in a circle of radius 8 cm, you step the compass around the circle. Which opening do you keep?
1. 8 cm, the radius of the circle
2. 16 cm, the diameter
3. Any opening, as long as it never changes
To inscribe a regular hexagon in a circle of radius 7 cm, you step the compass around the circle. Which opening do you keep?
1. 7 cm, the radius of the circle
2. 14 cm, the diameter
3. Any opening, as long as it never changes
To inscribe a regular hexagon in a circle of radius 4 cm, you step the compass around the circle. Which opening do you keep?
1. 4 cm, the radius of the circle
2. 8 cm, the diameter
3. Any opening, as long as it never changes
To inscribe a regular hexagon in a circle of radius 9 cm, you step the compass around the circle. Which opening do you keep?
1. 9 cm, the radius of the circle
2. 18 cm, the diameter
3. Any opening, as long as it never changes
To inscribe a regular hexagon in a circle of radius 6 cm, you step the compass around the circle. Which opening do you keep?
1. 6 cm, the radius of the circle
2. 12 cm, the diameter
3. Any opening, as long as it never changes
To inscribe a regular hexagon in a circle of radius 5 cm, you step the compass around the circle. Which opening do you keep?
1. 5 cm, the radius of the circle
2. 10 cm, the diameter
3. Any opening, as long as it never changes
To inscribe a regular hexagon in a circle of radius 3 cm, you step the compass around the circle. Which opening do you keep?
1. 3 cm, the radius of the circle
2. 6 cm, the diameter
3. Any opening, as long as it never changes
A regular hexagon is constructed inside a circle of radius 4 cm, with its vertices on the circle. What is its perimeter, in cm?Not to scale
Translate the point $A(-4, -4)$ by 2 units right and 1 units down. Tap its image $A'$ .
A translation takes $(-3, 0)$ to $(0, 5)$ . By how many units does it move points horizontally (positive = right)?
A polygon with 9 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
A polygon with 6 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
A polygon with 5 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
A polygon with 3 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
A polygon with 4 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
A polygon with 8 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
A polygon with 7 sides is translated. What changes?
1. Only its position: lengths and angles stay the same
2. Its side lengths
3. Its angles
Translate triangle ABC 2 right and 2 down. Tap the images A′, B′ and C′.
Reflect $A(3, 2)$ across the $x$ -axis. Tap its image.
Reflect $A(5, -1)$ across the line $y = x$ . Tap its image.
A point is 5 units from a line of reflection. How far is it from its image?
Reflect triangle ABC across the $y$ -axis. Tap the images A′, B′ and C′.
Rotate $A(1, 3)$ by $90^\circ$ counterclockwise about the origin. Tap its image.
Rotate $A(-2, -1)$ by $180^\circ$ about the origin. Tap its image.
A figure is rotated 7 times by $90^\circ$ in the same direction. What single rotation, between $0^\circ$ and $360^\circ$ , gives the same result? (degrees)
Rotate triangle ABC by 90° counterclockwise about the origin. Tap the images A′, B′ and C′.
What is the smallest positive angle of rotation that maps a regular polygon with 8 sides onto itself? (degrees)Not to scale
How many lines of symmetry does a regular polygon with 4 sides have?Not to scale
A rectangle 4 cm by 6 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
A rectangle 6 cm by 8 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
A rectangle 8 cm by 10 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
A rectangle 5 cm by 7 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
A rectangle 9 cm by 11 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
A rectangle 3 cm by 5 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
A rectangle 7 cm by 9 cm (not a square). Which transformations map it onto itself?
1. Reflections across its two midlines, and a 180° rotation about its center
2. Reflections across its diagonals
3. A 90° rotation
Two angles of a triangle measure $32^\circ$ and $20^\circ$ . Find the third angle, in degrees.
Two lines cross. One angle measures $30^\circ$ . Find the angle vertically opposite it, in degrees.
A transversal crosses two parallel lines and makes a $33^\circ$ angle with the first. Find the co-interior (same-side interior) angle it makes with the second line, in degrees.
$\triangle ABC \cong \triangle DEF$ 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

Answers

1. With the compass point on A, draw an arc with a radius of more than half of AB 2. Keep the same opening; with the point on B, draw an arc that crosses the first one twice 3. Label the two crossing points P and Q 4. Draw the line through P and Q with the straightedge
P and Q are each as far from A as from B, and such points lie on the perpendicular bisector
8 cm, the radius of the circle
$24$
$(-2, -5)$
$3$
Only its position: lengths and angles stay the same
$(-3, -2),\ (0, -2),\ (-2, 0)$
$(3, -2)$
$(-1, 5)$
$10$
$(-4, 3),\ (-7, 3),\ (-5, 5)$
$(-3, 1)$
$(2, 1)$
$270$
$(-3, 3),\ (-3, 6),\ (-5, 4)$
$45$
$4$
Reflections across its two midlines, and a 180° rotation about its center
$128$
$30$
$147$
$3$
$97$
$TU$
SAS
Not necessarily: side-side-angle can give two different triangles
Not necessarily: they have the same shape but may differ in size