# Lesson 4

Congruent Triangles, Part 2

### Problem 1

Match each statement using only the information shown in the pairs of congruent triangles.

### Solution

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### Problem 2

Sketch the unique triangles that can be made with angle measures $$40^{\circ}$$ and $$100^{\circ}$$ and side length 3. How do you know you have sketched all possibilities?

### Solution

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### Problem 3

What is the least amount of information that you need to construct a triangle congruent to this one?

### Solution

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### Problem 4

Triangle $$ABC$$ is congruent to triangle $$EDF$$. So, Mai knows that there is a sequence of rigid motions that takes $$ABC$$ to $$EDF$$.

Select all true statements after the transformations:

A:

Angle $$A$$ coincides with angle $$E$$.

B:

Angle $$B$$ coincides with angle $$F$$.

C:

Segment $$AB$$ coincides with segment $$EF$$.

D:

Segment $$BC$$ coincides with segment $$DF$$.

E:

Segment $$AC$$ coincides with segment $$ED$$.

### Solution

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(From Unit 2, Lesson 3.)

### Problem 5

A rotation by angle $$ACE$$ using point $$C$$ as the center takes triangle $$CBA$$ onto triangle $$CDE$$.

1. Explain why the image of segment $$CB$$ lines up with segment $$CD$$.
2. Explain why the image of $$B$$ coincides with $$D$$.
3. Is triangle $$ABC$$ congruent to triangle $$EDC$$? Explain your reasoning.

### Solution

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(From Unit 2, Lesson 3.)

### Problem 6

Line $$EF$$ is a line of symmetry for figure $$ABECDF$$. Clare says that $$ABEF$$ is congruent to $$CDFE$$ because sides $$AB$$ and $$CD$$ are corresponding.

1. Why is Clare's congruence statement incorrect?
2. Write a correct congruence statement for the quadrilaterals.

### Solution

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(From Unit 2, Lesson 2.)

### Problem 7

Triangle $$HEF$$ is the image of triangle $$HGF$$ after a reflection across line $$FH$$. Select all statements that must be true.

A:

Triangle $$FGH$$ is congruent to triangle $$FEH$$.

B:

Triangle $$EFH$$ is congruent to triangle $$GFH$$.

C:

Angle $$HFE$$ is congruent to angle $$FHG$$.

D:

Angle $$EFG$$ is congruent to angle $$EHG$$.

E:

Segment $$EH$$ is congruent to segment $$FG$$.

F:

Segment $$GH$$ is congruent to segment $$EH$$.

### Solution

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(From Unit 2, Lesson 2.)

### Problem 8

When rectangle $$ABCD$$ is reflected across line $$EF$$, the image is $$BADC$$. How do you know that segment $$AD$$ is congruent to segment $$BC$$?

A:

A rectangle has 2 pairs of parallel sides.

B:

Any 2 sides of a rectangle are congruent.

C:

Corresponding parts of congruent figures are congruent.

D:

Congruent parts of congruent figures are corresponding.

### Solution

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(From Unit 2, Lesson 1.)

### Problem 9

This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.

### Solution

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(From Unit 1, Lesson 22.)