Question

a pair of quadrilaterals are similar. which statements about the quadrilaterals must be true? select two correct answers. the opposite sides of the quadrilaterals must be congruent. the corresponding angles of the quadrilaterals must each be right angles. the corresponding side lengths of the quadrilaterals must be proportional. the corresponding angles of the quadrilaterals must be congruent.

Explanation:

Step1: Recall the definition of similar quadrilaterals

Similar quadrilaterals have the property that their corresponding angles are congruent and their corresponding side lengths are proportional.

Step2: Analyze each option

• Option 1: The corresponding angles of the quadrilaterals must be congruent

By the definition of similar polygons (including quadrilaterals), if two quadrilaterals are similar, their corresponding angles are congruent.

• Option 2: The corresponding side lengths of the quadrilaterals must be proportional

For similar polygons, the ratios of the lengths of corresponding sides (corresponding side lengths) are equal, which means they are proportional.

• Option 3: The corresponding angles of the quadrilaterals must each be right angles

This is not a requirement for general similar quadrilaterals. For example, two similar parallelograms (that are not rectangles) have congruent non - right corresponding angles.

• Option 4: The opposite sides of the quadrilaterals must be congruent

This is a property of parallelograms (a specific type of quadrilateral) but not a general property of similar quadrilaterals. Similar quadrilaterals only require corresponding side - length proportionality and corresponding angle congruence, not that opposite sides of each quadrilateral are congruent.

Answer:

The corresponding angles of the quadrilaterals must be congruent; The corresponding side lengths of the quadrilaterals must be proportional.