# Lesson 13

### Problem 1

Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.

1. Draw a diagram of the situation.
2. Mark the given information.
3. Restate the conjecture as a specific statement using the diagram.

### Solution

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### Problem 2

In quadrilateral $$ABCD$$, $$AD$$ is congruent to $$BC$$, and $$AD$$ is parallel to $$BC$$. Show that $$ABCD$$ is a parallelogram.

### Solution

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### Problem 3

$$ABDE$$ is an isosceles trapezoid. Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles trapezoid are congruent.

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### Solution

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(From Unit 2, Lesson 12.)

### Problem 4

Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.

A:

In parallelogram $$EFGH$$, show triangle $$HEF$$ is congruent to triangle $$FGH$$.

B:

In parallelogram $$EFGH$$, show triangle $$EKH$$ is congruent to triangle $$GKF$$.

C:

In parallelogram $$EFGH$$, show $$EK$$ is congruent to $$KG$$ and $$FK$$ is congruent to $$KH$$.

D:

In quadrilateral $$EFGH$$ with $$GH$$ congruent to $$FE$$ and $$EH$$ congruent to $$FG$$, show $$EFGH$$ is a parallelogram.

### Solution

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(From Unit 2, Lesson 12.)

### Problem 5

Is triangle $$EJH$$ congruent to triangle $$EIH$$?

### Solution

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(From Unit 2, Lesson 11.)

### Problem 6

Select all true statements based on the diagram.

A:

Segment $$DC$$ is congruent to segment $$AB$$.

B:

Segment $$DA$$ is congruent to segment $$CB$$.

C:

Line $$DC$$ is parallel to line $$AB$$.

D:

Line $$DA$$ is parallel to line $$CB$$.

E:

Angle $$CBE$$ is congruent to angle $$DEA$$.

F:

Angle $$CEB$$ is congruent to angle $$DEA$$.

### Solution

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(From Unit 2, Lesson 10.)

### Problem 7

Which conjecture is possible to prove?

A:

If the four angles in a quadrilateral are congruent to the four angles in another quadrilateral, then the two quadrilaterals are congruent.

B:

If the four sides in a quadrilateral are congruent to the four sides in another quadrilateral, then the two quadrilaterals are congruent.

C:

If the three angles in a triangle are congruent to the three angles in another triangle, then the two triangles are congruent.

D:

If the three sides in a triangle are congruent to the three sides in another triangle, then the two triangles are congruent.

### Solution

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(From Unit 2, Lesson 5.)