IM Geo.2.9 Practice: Side-Side-Side Triangle Congruence

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 [math]WXYZ[/math], show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.

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 [math]WY[/math] bisects angles [math]ZWX[/math] and [math]ZYX[/math]?

WXYZ is a kite.

Angle [math]WXY[/math] has a measure of 133 degrees and angle [math]ZWX[/math] has a measure of 60 degrees. Find the measure of angle [math]ZYW[/math].

Each statement is always true.

Select [b]all[/b] 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 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. Statement: If 2 angles are vertical, then they are congruent. Converse: If 2 angles are congruent, then they are vertical. Statement: If 2 angles form a straight angle, then they are supplementary. Converse: If 2 angles are supplementary, then they form a straight angle.

Prove triangle [math]ABD[/math] is congruent to triangle [math]CDB[/math].

Triangles ACD and BCD are isosceles.

[size=150]Angle [math]DBC[/math] has a measure of 84 degrees and angle [math]BDA[/math] has a measure of 24 degrees. [/size][br]Find the measure of angle [math]BAC[/math].

Reflect right triangle ABC across line AB.

Classify triangle [math]CAC'[/math] according to its side lengths. Explain how you know.