ISEE Upper Level Math : Isosceles Triangles

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #1 : Acute / Obtuse 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:

Explanation:

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 #2 : Acute / Obtuse Isosceles Triangles

The triangles are similar. Solve for .

Question_12

Possible Answers:

Correct answer:

Explanation:

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

Cross-multiply:

Example Question #31 : Geometry

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

Possible Answers:

Correct answer:

Explanation:

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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