Question

1. a quadrilateral has a line of symmetry. select all conclusions that must be true. (from unit 1, lesson 15.) all sides of the quadrilateral have the same length. all angles of the quadrilateral have the same measure. two sides of the quadrilateral have the same length. two angles of the quadrilateral have the same measure. no sides of the quadrilateral have the same length.

Explanation:

A line of symmetry means that one - half of the figure is the mirror image of the other half.

• For the side - length claim: A rectangle (a quadrilateral with a line of symmetry) has opposite sides equal, not all sides equal. So “All sides of the quadrilateral have the same length” is false.
• For the angle - measure claim: A kite (a quadrilateral with a line of symmetry) has two pairs of adjacent sides equal and one pair of opposite angles equal. So “All angles of the quadrilateral have the same measure” is false.
• For the non - equal side claim: Since there is a line of symmetry, at least two sides (the ones that are mirror images) must be equal. So “No sides of the quadrilateral have the same length” is false.
• For the two - side - length claim: By the property of line of symmetry (reflection), the sides that are mirror images of each other are equal. So “Two sides of the quadrilateral have the same length” is true.
• For the two - angle - measure claim: The angles that are mirror images of each other are equal. So “Two angles of the quadrilateral have the same measure” is true.

Answer:

C. Two sides of the quadrilateral have the same length, D. Two angles of the quadrilateral have the same measure.