Lesson 17

Working with Rigid Transformations

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Quadrilateral \(ABCD\) is congruent to quadrilateral \(A’B’C’D’\). Describe a sequence of rigid motions that takes \(A\) to \(A’\), \(B\) to \(B’\), \(C\) to \(C’\), and \(D\) to \(D’\).

Congruent quadrilaterals A B C D and A prime B prime C prime D prime. 

Problem 2

Select all transformations that must take any point \(A\) to any point \(B\).

A:

Rotation of \(180^\circ\)around \(A\)

B:

Rotation of \(180^\circ\)around \(B\)

C:

Rotation of \(180^\circ\)around the midpoint of segment \(AB\)

D:

Reflection across the line \(AB\)

E:

Reflection across the perependicular bisector of segment \(AB\)

F:

Translation by the directed line segment \(AB\)

G:

Translation by the directed line segment \(BA\)

Problem 3

Triangle \(ABC\) is congruent to triangle \(A’B’C’\). Describe a sequence of rigid motions that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\).

Congruent triangles A B C and A prime B prime C prime.

 

Problem 4

A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this.

A:

All sides of the triangle have the same length.

B:

All angles of the triangle have the same measure.

C:

All rotations take one half of the triangle to the other half of the triangle.

D:

It is a right triangle.

E:

None of the sides of the triangle have the same length.

F:

None of the angles of the triangle have the same measure.

(From Geometry, Unit 1, Lesson 16.)

Problem 5

Select all the angles of rotation that produce symmetry for this flower.

Flower on polar grid.
A:

30

B:

45

C:

60

D:

90

E:

120

F:

135

G:

180

(From Geometry, Unit 1, Lesson 16.)

Problem 6

A right triangle has a line of symmetry. Select all conclusions that must be true.

A:

All sides of the triangle have the same length.

B:

All angles of the triangle have the same measure.

C:

Two sides of the triangle have the same length.

D:

Two angles of the triangle have the same measure.

E:

No sides of the triangle have the same length.

F:

No angles of the triangle have the same measure.

(From Geometry, Unit 1, Lesson 15.)

Problem 7

In quadrilateral \(BADC\), \(AB=AD\) and \(BC=DC\). The line \(AC\) is a line of symmetry for this quadrilateral. Based on the line of symmetry, explain why angles \(ACB\) and \(ACD\) have the same measure.

Quadrilateral B A D C.
(From Geometry, Unit 1, Lesson 15.)

Problem 8

Which of these constructions would construct a line of reflection that takes the point \(A\) to point \(B\)?

A:

Construct the midpoint of segment $AB$.

B:

Construct the perpendicular bisector of segment $AB$.

C:

Construct a line tangent to circle $A$ with radius $AB$.

D:

Construct a vertical line passing through point $A$ and a horizontal line passing through point $B$.

(From Geometry, Unit 1, Lesson 11.)

Problem 9

Here is triangle \(POG\). Match the description of the rotation with the image of \(POG\) under that rotation.

Triangle P O G on isometric grid. P O and O G are both 2 units long. O G is vertical.
(From Geometry, Unit 1, Lesson 13.)