Question

22 which of the following conjectures is illustrated by the diagram? a the sum of the measures of the interior angles of a triangle is 180° b the base angles of an isosceles triangle are congruent. c a point that lies on a perpendicular bisector of a line segment is equidistant from the line segments endpoints. d the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Explanation:

• Option A: The diagram does not show any calculation or indication related to the sum of interior angles of a triangle being \(180^{\circ}\).
• Option B: There is no clear indication of an isosceles triangle with base - angle congruence in the given diagram.
• Option C: The diagram shows a line segment \(AB\) and points \(C\) and \(D\) on the perpendicular bisector of \(AB\). By the property of the perpendicular bisector of a line segment, any point on the perpendicular bisector is equidistant from the endpoints of the line segment. So, \(CA = CB\) and \(DA=DB\).
• Option D: The diagram does not show any exterior - angle and its relation to remote interior angles.

Answer:

C. A point that lies on a perpendicular bisector of a line segment is equidistant from the line segment's endpoints.