# Thread: Proving Similarity With Triangles

1. ## Proving Similarity With Triangles

I still cannot prove this triangle being similar to the other one, if anyone can explain it that would be extremly grateful.

Many thanks

2. ## Re: Proving Similarity With Triangles

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. In other words, two triangles are similar if they have the same shape.

In this case, the two triangles have different shapes. AED is clearly an equilateral triangle, while ABC is an scalene one, so they aren't similar.

3. ## Re: Proving Similarity With Triangles

Hello, JohnyyMal!

The drawing is misleading. .(Mine is no better.)

$\text{Prove: }\:\Delta ABC \sim \Delta AED$

Code:
            A
o
*
*  *
*
*     * C
o
*     *  *
θ  *     *
*  *        *
*           *
B o              *
*
*                 *
θ  *
D o   *   *   *   *    o E

$\Delta ABC\text{ has: }\,\angle\theta\text{ and }\angle A.$

$\Delta AED\text{ has: }\,\angle\theta\text{ and }\angle A.$

. . Hence, their third angles are equal.

Therefore: . $\Delta ABC \sim \Delta AED\;\;\;(a.a.a.)$