Illustrative Mathematics - Geometry - Mathematics - Unit 2 - Lesson 9

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Last updated about 1 year ago

7 Questions

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.

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Mai has proven that triangle XYZ 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?

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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.

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

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

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.

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.

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Prove triangle ABD is congruent to triangle CDB.

DC  || AB

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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.

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

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This lesson is from Illustrative Mathematics. Geometry, Unit 2, Lesson 9. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/2/9/index.html ; accessed 29/July/2021.

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