Triangles ABC and BCD are each isosceles. If , what is the value of ?

If and are the lengths of two sides of a triangle, which of the following can be the length of the third side?

I.

II.

III.

Isosceles right triangle ABC has an area of . What is its perimeter?

What is the sum ?

In the isosceles triangle EFG above, angle FEG measures degrees and side FG measures centimeters. What is the length in centimeters, of side EG?

In triangle LMN above what is in terms of ?

What is the value of ?

In isosceles triangle XYZ above, angle XYZ measures degrees. What is the measure of angle XZY?

Starting from her home, Mirinda rides her bike in a straight line due south for kilometers, then turns and rides in a straight line due west for kilometers, at which point she stops. Assuming that she can ride in any direction with no barriers, what is the distance of her shortest route back home?

What is the area of Triangle XYZ?