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:

• For the first statement: An isosceles trapezoid can be divided into a rectangle and two congruent right - angled triangles by dropping perpendiculars from the endpoints of the shorter base to the longer base.
• For the second statement: A kite has two distinct pairs of adjacent sides equal. If we draw a diagonal, it can be divided into two congruent triangles. But it cannot be divided into a rectangle and a triangle.
• For the third statement: When a kite is divided into two congruent triangles (by its axis of symmetry - one of its diagonals), the height of the triangles is not found by dividing the width (the length of the other diagonal) by 2. The area formula for a kite is \(A=\frac{1}{2}d_1d_2\) (where \(d_1\) and \(d_2\) are the lengths of the diagonals). If we consider the two triangles formed by one diagonal \(d_1\), the base of each triangle is \(d_1\) and the sum of their heights is \(d_2\).
• For the fourth statement: A trapezoid is a quadrilateral with exactly one pair of parallel sides. A quadrilateral with two pairs of parallel opposite sides is a parallelogram.
• For the fifth statement: The area of a kite is \(A = \frac{1}{2}d_1d_2\) (where \(d_1\) and \(d_2\) are the lengths of the diagonals), not \(A=\text{length}\times\text{width}\) (which is the formula for the area of a rectangle).

Answer:

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