# Side-Side-Side Triangle Congruence

# Side-Side-Side Triangle Congruence

##### Problem 1

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.

##### Problem 2

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 $ZYX$?

##### Problem 3

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 $ZYW$.

##### Problem 4

4) Each statement is always true. Select **all** statements for which the converse is also always true. Write each corresponding letter in the answer box and separate letters with commas.

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.

##### Problem 5

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

Given: $DC \parallel AB$

##### Problem 6

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 $BAC$.

Given: $\overline{AD} \cong \overline{AC}$ and $\overline{BD} \cong \overline{BC}$

##### Problem 7

7) Reflect right triangle $ABC$ across line $AB$.

8) Classify triangle $CAC'$ according to its side lengths.

9) Explain how you know.