Lesson 11

Defining Reflections

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Problem 1

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

A:

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

B:

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

C:

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

D:

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

Solution

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Problem 2

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

What can you conclude about \(P\)?

Line L, with endpoints at the bottom left and top right

 

Solution

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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.

\(m \perp \ell\)

Perpendicular lines L and M, intersecting at point P. L is horizontal, m is vertical.

 

Solution

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Problem 4

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

A:
Congruent triangles A B C and A prime B prime C prime.
B:
Congruent triangles A B C and A prime B prime C prime.
C:
Triangles A B C and A prime B prime C prime. Triangle A B C is larger.
D:
Congruent triangles A B C and A prime B prime C prime.

Solution

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(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 \(D’\):

Triangles A B C and A prime B prime C prime. Point D is located on side A C.

Solution

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(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 \(B\).

Three points, point A to the left of point B, point C above both points A and B.

Solution

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(From Unit 1, Lesson 9.)

Problem 7

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

Solution

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(From Unit 1, Lesson 7.)