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

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.

Tags

7.G.2

G.CO.8

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?

Tags

7.G.2

G.CO.8

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.

Tags

7.G.2

G.CO.8

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.

Tags

7.G.2

G.CO.8

Prove triangle ABD is congruent to triangle CDB.DC || AB

Tags

7.G.2

G.CO.8

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.

Tags

7.G.2

G.CO.8