### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : Isosceles Triangles

Two sides of an isosceles triangle have lengths 3 feet and 4 feet. Which of the following could be the length of the third side?

**Possible Answers:**

**Correct answer:**

An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 3 feet or 4 feet would make the triangle meet this criterion.

3 feet is equal to inches, and 4 feet is equal to inches. We choose 36 inches, since that, but not 48 inches, is a choice.

### Example Question #1 : Acute / Obtuse Isosceles Triangles

The triangles are similar. Solve for .

**Possible Answers:**

**Correct answer:**

Because the triangles are similar, proportions can be used to solve for the length of the side:

Cross-multiply:

### Example Question #2 : Isosceles Triangles

One of the base angles of an isosceles triangle is . Give the measure of the vertex angle.

**Possible Answers:**

**Correct answer:**

The base angles of an isosceles triangle are always equal. Therefore both base angles are .

Let the measure of the third angle. Since the sum of the angles of a triangle is , we can solve accordingly:

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