# Side-Side-Side Triangle Congruence

ID: gabip-gonof Illustrative Math
Subject: Geometry

# Side-Side-Side Triangle Congruence

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##### 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.