# 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 rectangle has 2 pairs of parallel sides.

Any 2 sides of a rectangle are congruent.

Congruent parts of congruent figures are corresponding.

Corresponding parts of congruent figures are congruent.

### Solution

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### 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.

\(EFGH\) is a rectangle.

\(EFGH\) has 4 congruent sides.

Diagonal \(FH\) bisects angles \(EFG\) and \(EHG\).

Diagonal \(FH\) is perpendicular to side \(FE\).

Angle \(FEH\) is congruent to angle \(FGH\).

### Solution

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### Problem 3

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

### Solution

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### Problem 4

Triangles \(FAD\) and \(DCE\) are translations of triangle \(ABC\)

Select **all** the statements that *must* be true.

Points \(B\), \(A\), and \(F\) are collinear.

The measure of angle \(BCA\) is the same as the measure of angle \(CED\).

Line \(AD\) is parallel to line \(BC\).

The measure of angle \(CED\) is the same as the measure of angle \(FAD\).

The measure of angle \(DAC\) is the same as the measure of angle \(BCA\).

Triangle \(ADC\) is a reflection of triangle \(FAD\).

### Solution

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(From Unit 1, Lesson 21.)### Problem 5

Triangle \(ABC\) is congruent to triangles \(BAD\) and \(CEA\).

- Explain why points \(D\), \(A\), and \(E\) are collinear.
- Explain why line \(DE\) is parallel to line \(BC\).

### Solution

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(From Unit 1, Lesson 21.)### Problem 6

- Identify a figure that is the result of a rigid transformation of quadrilateral \(ABCD\).
- Describe a rigid transformation that would take \(ABCD\) to that figure.

### Solution

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(From Unit 1, Lesson 18.)