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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.

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
$128$
$30$
$147$