# Lesson 12

### Problem 1

Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that $$EFGH$$ is a parallelogram and angle $$HEF$$ is right, which reasoning about angles will help her prove that angle $$FGH$$ is also a right angle?

A:

Corresponding angles are congruent when parallel lines are cut by a transversal.

B:

Opposite angles in a parallelogram are congruent.

C:

Vertical angles are congruent.

D:

The base angles of an isosceles triangle are congruent.

### Problem 2

$$ABDE$$ is an isosceles trapezoid. Select all pairs of congruent triangles.

​​​​​​

A:

Triangle $$ABE$$ and triangle $$DBE$$

B:

Triangle $$ABD$$ and triangle $$DAE$$

C:

Triangle $$ABE$$ and triangle $$BAD$$

D:

Triangle $$AED$$ and triangle $$BDE$$

E:

Triangle $$EAB$$ and triangle $$EDB$$

### Problem 3

Match each conjecture with the rephrased statement of proof connected to the diagram.

### Problem 4

Which of the following criteria always proves triangles congruent? Select all that apply.

A:

Corresponding congruent Angle-Side-Angle

B:

Corresponding congruent Side-Angle-Side

C:

Corresponding congruent Side-Side-Angle

D:

3 congruent sides

E:

2 congruent sides

F:

3 congruent angles

### Solution

(From Unit 2, Lesson 11.)

### Problem 5

Select all true statements based on the diagram.

A:

Segment $$EB$$ is congruent to segment $$AD$$.

B:

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

C:

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

D:

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

E:

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

F:

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

G:

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

### Solution

(From Unit 2, Lesson 10.)

### Problem 6

Diego states that diagonal $$WY$$ bisects angles $$ZWX$$ and $$ZYX$$. Is he correct? Explain your reasoning.

### Solution

Sketch the unique triangles that can be made with angle measures $$80^{\circ}$$ and $$20^{\circ}$$ and side length 5. How do you know you have sketched all possibilities?