Question

question 2 which (3) shapes create two identical triangles when cut by a diagonal? select all that apply. a rectangle b square c trapezoid d parallelogram

Explanation:

Step1: Analyze rectangle

A rectangle has opposite sides equal and all angles 90 degrees. When a diagonal is drawn, two congruent right - angled triangles are formed by SSS (Side - Side - Side) congruence criterion as the opposite sides are equal and the diagonal is common.

Step2: Analyze square

A square is a special rectangle with all sides equal. When a diagonal is drawn, two congruent right - angled isosceles triangles are formed. By SSS congruence (since all sides of the square are equal and the diagonal is common), the two triangles are identical.

Step3: Analyze trapezoid

A trapezoid has one pair of parallel sides. When a diagonal is drawn, the two triangles formed are not congruent in general as the non - parallel sides and angles are not equal in a non - isosceles trapezoid, and even in an isosceles trapezoid, the triangles are not congruent.

Step4: Analyze parallelogram

A parallelogram has opposite sides equal. When a diagonal is drawn, two congruent triangles are formed. By SSS congruence (opposite sides are equal and the diagonal is common), the two triangles are identical.

Answer:

A. rectangle, B. square, D. parallelogram