Question

Write a coordinate proof for the statement: The segments joining base vertices to the midpoints of the legs of an isosceles triangle are congruent. Given points: B(20,26), D(a,b), E(3a,b), C(42,0).

A) The statement is false.
B) Prove the statement using coordinate geometry.
C) There is not enough information to prove or disprove the statement.
D) Coordinate proof is not applicable here.

Answer 1

To prove that the segments joining the base vertices to the midpoints of the legs of an isosceles triangle are congruent, you can use coordinate geometry to find the coordinates of the midpoints and calculate the distance between them.

Step-by-step explanation:

To prove that the segments joining the base vertices to the midpoints of the legs of an isosceles triangle are congruent, we will use coordinate geometry.

1. Start by finding the coordinates of the midpoints of the legs. The midpoint of BD is (20 + a)/2, (26 + b)/2, and the midpoint of CE is (42 + 3a)/2, b/2.
2. Calculate the distance between the two midpoints using the distance formula √((x2-x1)^2 + (y2-y1)^2).
3. Simplify the expression and show that the distance between the midpoints is equal.

Therefore, the segments joining the base vertices to the midpoints of the legs of an isosceles triangle are congruent.