Question

In isosceles triangle DAC, AD is congruent to AC.Kiran knows that the base angles of an isosceles triangle are congruent. What additional information does Kiran need to know in order to show that AB is a perpendicular bisector of segment CD?

Answer 1

To prove AB is a perpendicular bisector of CD in triangle DAC, Kiran needs to know that AB bisects CD and forms a right angle at the point of intersection.

Step-by-step explanation:

To show that segment AB is a perpendicular bisector of segment CD in isosceles triangle DAC, where AD is congruent to AC, Kiran would need to know two additional pieces of information:

1. That AB intersects CD at its midpoint, thereby bisecting CD.
2. That the angle formed by AB and CD at their intersection is a right angle (90 degrees), demonstrating perpendicularity.

Once these two criteria are met, it can be concluded that AB is indeed a perpendicular bisector of CD. Knowing that the base angles of an isosceles triangle are congruent is a starting point, but by itself, it does not provide enough information to determine the relationship between AB and CD.