# Lesson 11

Defining Reflections

### Problem 1

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

Construct the perpendicular bisector of segment \(AB\).

Construct a line through \(B\) perpendicular to segment \(AB\).

Construct the line passing through \(A\) and \(B\).

Construct a line parallel to line \(AB\).

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

A point \(P\) stays in the same location when it is reflected over line \(\ell\).

What can you conclude about \(P\)?

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

Lines \(\ell\) and \(m\) are perpendicular with point of intersection \(P\).

Noah says that a 180 degree rotation, with center \(P\), has the same effect on points in the plane as reflecting over line \(m\). Do you agree with Noah? Explain your reasoning.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 4

Here are 4 triangles that have each been transformed by a different transformation. Which transformation is *not* a rigid transformation?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 10.)### Problem 5

There is a sequence of rigid transformations that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\). The same sequence takes \(D\) to \(D’\). Draw and label \(D’\):

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 10.)### Problem 6

Here are 3 points in the plane. Explain how to determine whether point \(C\) is closer to point \(A\) or point \(B\).

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 9.)### Problem 7

Diego says a quadrilateral with 4 congruent sides is always a regular polygon. Mai say it never is one. Do you agree with either of them?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 1, Lesson 7.)