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