Question

12. triangle KMP is isosceles with KM = KP. MX and PY are angle bisectors.

a. Is there enough information to prove triangle WMP is an isosceles
triangle? Explain.

b. Can you conclude that MX and PY are medians?

c. What one additional piece of information would allow you to prove
that MX and PY are altitudes?


triangle below

Answer 1

A: An isosceles triangle is defined as having 2 sides measurements that are equal, and they have equal base angles as a result. If KM and KP are equal then they fit the definition of an isosceles triangle. If KMP is an isosceles triangle and they both have the same base angles. If the base angles are bisected they have the same base angle measurement making WMP also an isosceles triangle

B: Yes, because the angle bisectors of MX and MP would also bisect the sides making them both medians.

C to prove that they were Altitudes we would need to know that the base angles of KMP are 60 degrees. if they are 60 degrees they would create two 30-60-90 triangles with the 90 degrees going from the center of the side directly up, perpendicularly to the altitude. (this would also make the triangle an equilateral triangle)