Side-Side-Side Triangle Congruence

ID: gabip-gonof
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

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 WXYZWXYZ, show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.

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Problem 2

2) Mai has proven that triangle WYZWYZ is congruent to triangle WYXWYX using the Side-Side-Side Triangle Congruence Theorem. Why can she now conclude that diagonal WYWY bisects angles ZWXZWX and ZYXZYX?

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Problem 3

3) WXYZWXYZ is a kite. Angle WXYWXY has a measure of 133 degrees and angle ZWXZWX has a measure of 60 degrees. Find the measure of angle ZYWZYW.

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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 ABDABD is congruent to triangle CDBCDB .

Given: DCABDC \parallel AB

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Problem 6

6) Triangles ACDACD and BCDBCD are isosceles. Angle DBCDBC has a measure of 84 degrees and angle BDABDA has a measure of 24 degrees. Find the measure of angle BACBAC.

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

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Problem 7

7) Reflect right triangle ABCABC across line ABAB.

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8) Classify triangle CACCAC' according to its side lengths.

9) Explain how you know.