# Lesson 10

Rigid Transformations

### Problem 1

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

A:
B:
C:
D:

### Solution

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### Problem 2

What is the definition of congruence?

A:

If two figures have the same shape, then they are congruent.

B:

If two figures have the same area, then they are congruent.

C:

If there is a sequence of transformations taking one figure to another, then they are congruent.

D:

If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.

### Solution

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### Problem 3

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

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### Problem 4

Three schools are located at points $$A$$, $$B$$, and $$C$$. The school district wants to locate its new stadium at a location that will be roughly the same distance from all 3 schools. Where should they build the stadium? Explain or show your reasoning.

### Solution

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(From Unit 1, Lesson 9.)

### Problem 5

To construct a line passing through point $$C$$ that is parallel to the line $$AB$$, Han constructed the perpendicular bisector of $$AB$$ and then drew line $$CD$$.

Is $$CD$$ guaranteed to be parallel to $$AB$$? Explain how you know.

### Solution

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(From Unit 1, Lesson 6.)

### Problem 6

This diagram is a straightedge and compass construction of a line perpendicular to line $$AB$$ passing through point $$C$$. Select all the statements that must be true.

A:

$$AD=BD$$

B:

$$EC=AD$$

C:

$$AC=DC$$

D:

$$EA=ED$$

E:

$$ED=DB$$

F:

$$CB=AD$$

### Solution

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(From Unit 1, Lesson 5.)