Question

1. a quadrilateral has a line of symmetry.

select all conclusions that must be true.
a. all sides of the quadrilateral have b. all angles of the quadrilateral have
the same length. the same measure.
c. two sides of the quadrilateral have d. two angles of the
quadrilateral have the same
the same length. measure.
e. no sides of the quadrilateral have f. no angles of the quadrilateral have
the same length. the same measure.

Explanation:

Step1: Analyze the property of line of symmetry

A line of symmetry divides a figure into two congruent parts. For a quadrilateral with a line of symmetry, the parts on either side of the line of symmetry are mirror - images.

Step2: Check each option

• Option A: A quadrilateral with a line of symmetry (e.g., an isosceles trapezoid) does not have all sides equal. So, this option is false.
• Option B: A quadrilateral with a line of symmetry (e.g., an isosceles trapezoid) does not have all angles equal. So, this option is false.
• Option C: Due to the mirror - image property of the line of symmetry, at least two sides must be equal. For example, in an isosceles trapezoid, the non - parallel sides are equal. So, this option is true.
• Option D: Because of the mirror - image property of the line of symmetry, at least two angles (the angles that are mirror - images of each other) must be equal. So, this option is true.
• Option E: Since there is a line of symmetry, there must be at least two sides that are equal (as they are mirror - images). So, this option is false.
• Option F: Since there is a line of symmetry, there must be at least two angles that are equal (as they are mirror - images). So, this option is false.

Answer:

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