# Lesson 1

Congruent Parts, Part 1

### Problem 1

When rectangle $$ABCD$$ is reflected across line $$EF$$, the image is $$DCBA$$. How do you know that segment $$AB$$ is congruent to segment $$DC$$?

A:

A rectangle has 2 pairs of parallel sides.

B:

Any 2 sides of a rectangle are congruent.

C:

Congruent parts of congruent figures are corresponding.

D:

Corresponding parts of congruent figures are congruent.

### Problem 2

Triangle $$FGH$$ is the image of isosceles triangle $$FEH$$ after a reflection across line $$HF$$. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.

A:

$$EFGH$$ is a rectangle.

B:

$$EFGH$$  has 4 congruent sides.

C:

Diagonal $$FH$$ bisects angles $$EFG$$ and $$EHG$$.

D:

Diagonal $$FH$$ is perpendicular to side $$FE$$.

E:

Angle $$FEH$$ is congruent to angle $$FGH$$.

### Problem 3

Reflect right triangle $$ABC$$ across line $$BC$$. Classify triangle $$ACA’$$ according to its side lengths. Explain how you know.

### Problem 4

Triangles $$FAD$$ and $$DCE$$ are translations of triangle $$ABC$$

Select all the statements that must be true.

A:

Points $$B$$, $$A$$, and $$F$$ are collinear.

B:

The measure of angle $$BCA$$ is the same as the measure of angle $$CED$$.

C:

Line $$AD$$ is parallel to line $$BC$$.

D:

The measure of angle $$CED$$ is the same as the measure of angle $$FAD$$.

E:

The measure of angle $$DAC$$ is the same as the measure of angle $$BCA$$.

F:

Triangle $$ADC$$ is a reflection of triangle $$FAD$$.

### Solution

(From Unit 1, Lesson 21.)

### Problem 5

Triangle $$ABC$$ is congruent to triangles $$BAD$$ and $$CEA$$.

1. Explain why points $$D$$, $$A$$, and $$E$$ are collinear.
2. Explain why line $$DE$$ is parallel to line $$BC$$.

### Solution

1. Identify a figure that is the result of a rigid transformation of quadrilateral $$ABCD$$.
2. Describe a rigid transformation that would take $$ABCD$$ to that figure.