Question

which statements about special quadrilaterals are true? choose two correct answers. an isosceles trapezoid can be broken into a rectangle and two triangles. a kite can be broken into two triangles or a rectangle and a triangle. after breaking a kite into two triangles of the same size and shape, find the height of the triangles by dividing the width by 2. a trapezoid is a quadrilateral with two pairs of parallel opposite sides. the area of a kite can be found by multiplying the length times the width.

Explanation:

Step1: Analyze the first statement

An isosceles trapezoid can be divided into a rectangle and two congruent triangles. This is a valid geometric decomposition.

Step2: Analyze the second statement

A kite cannot be broken into a rectangle and a triangle. When a kite is divided, it is usually into two congruent triangles.

Step3: Analyze the third statement

When a kite is broken into two congruent triangles, the height of the triangles is not found by dividing the width by 2. The formula for the area of a kite is \(A=\frac{1}{2}d_1d_2\) (where \(d_1\) and \(d_2\) are the diagonals).

Step4: Analyze the fourth statement

A trapezoid has only one pair of parallel sides. A quadrilateral with two pairs of parallel sides is a parallelogram.

Step5: Analyze the fifth statement

The area of a kite is \(A = \frac{1}{2}d_1d_2\), not \(A=\text{length}\times\text{width}\) (which is for rectangles).

Answer:

An isosceles trapezoid can be broken into a rectangle and two triangles.