write a two column proof. given: ab is congruent to ed, ca is congruent to ce; ac bisects bd. Prove abc is congruent edc.
1 answer:
Given that, AB ≅ ED, CA ≅ CE, and AC bisects BD, the two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.
<h3>What is the SSS Congruence Theorem?</h3>The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information:
- AB ≅ ED
- CA ≅ CE
- AC bisects BD
Since AC bisects BD, therefore the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
Therefore, it implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), which meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
- The two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.
Learn more about the SSS Congruence Theorem on:
You might be interested in
Answer:
feet
Step-by-step explanation:
Consider the attached figure.
An isosceles triangle is a triangle in which two sides are equal.
feet
According to Pythagoras theorem,
square of hypotenuse is equal to sum of squares of other two sides.
feet