In the diagram, BC⎯⎯⎯⎯⎯∥DE⎯⎯⎯⎯⎯ .

What is AE ?

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___ in.

THE ANSWER IS 18in

The length of AE is

Explanation:

From the figure, we can see that the two triangles ΔAED and ΔACB are similar. Thus, the legs of the triangle are proportional to each other.

Thus, we have,

Substituting the values of the sides from the image, we get,

Multiplying both sides of the equation by 6, we get,

Multiplying, we have,

Thus, the length of AE is

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc