Question

2. If two arcs in a circle have the same measure, what can you say about the quadrilateral formed by the four endpoints? Explain.

Answer 1

The quadrilateral is an isosceles trapezoid.

Explanation:

If we call the ends of the first arc A and B, and the ends of the second arc C and D (listed in the clockwise direction), then the following will be true:

• BC will be parallel to AD
• angles B and C will be congruent, as will angles A and D
• diagonals AC and BD will be congruent
• the perpendicular bisector of BC is the same line as the perpendicular bisector of AD. Said line is a line of symmetry for the quadrilateral.

All of these observations are consistent with ABCD being an isosceles trapezoid.