Isosceles Triangles - ISEE Upper Level Mathematics Achievement
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One of the base angles of an isosceles triangle is 
. Give the measure of the vertex angle.
One of the base angles of an isosceles triangle is
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:
The base angles of an isosceles triangle are always equal. Therefore both base angles are
Let
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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?
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?
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.
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
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The triangles are similar. Solve for 
.
The triangles are similar. Solve for
Because the triangles are similar, proportions can be used to solve for the length of the side:
Cross-multiply:
Because the triangles are similar, proportions can be used to solve for the length of the side:
Cross-multiply:
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