# Lesson 9

Side-Side-Side Triangle Congruence

### Problem 1

A kite is a quadrilateral which has 2 sides next to each other that are congruent and where the other 2 sides are also congruent. Given kite $$WXYZ$$, show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.

### Solution

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### Problem 2

Mai has proven that triangle $$WYZ$$ is congruent to triangle $$WYX$$ using the Side-Side-Side Triangle Congruence Theorem. Why can she now conclude that diagonal $$WY$$ bisects angles $$ZWX$$ and $$ZYX$$?

### Solution

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### Problem 3

$$WXYZ$$ is a kite. Angle $$WXY$$ has a measure of 133 degrees and angle $$ZWX$$ has a measure of 60 degrees. Find the measure of angle $$ZYW$$.

### Solution

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### Problem 4

Each statement is always true. Select all statements for which the converse is also always true.

A:

Statement: If 2 angles form a straight angle, then they are supplementary. Converse: If 2 angles are supplementary, then they form a straight angle.

B:

Statement: In an isosceles triangle, the base angles are congruent. Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.

C:

Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.

D:

Statement: If 2 angles are vertical, then they are congruent. Converse: If 2 angles are congruent, then they are vertical.

E:

Statement: If 2 lines are perpendicular, then they intersect to form 4 right angles. Converse: If 2 lines intersect to form 4 right angles, then they are perpendicular.

### Solution

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(From Unit 2, Lesson 8.)

### Problem 5

Prove triangle $$ABD$$ is congruent to triangle $$CDB$$.

### Solution

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(From Unit 2, Lesson 7.)

### Problem 6

Triangles $$ACD$$ and $$BCD$$ are isosceles. Angle $$DBC$$ has a measure of 84 degrees and angle $$BDA$$ has a measure of 24 degrees. Find the measure of angle $$BAC$$.

### Solution

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(From Unit 2, Lesson 6.)

### Problem 7

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

### Solution

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(From Unit 2, Lesson 1.)