ISEE Upper Level Quantitative : Acute / Obtuse Isosceles Triangles
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Example Questions
Example Question #1 : Isosceles Triangles
Two sides of a triangle have length 8 inches and 6 inches. Which of the following lengths of the third side would make the triangle isosceles?
All of the other choices are correct.
All of the other choices are correct.
An isosceles triangle, by definition, has two sides of equal length. Having the third side measure either 6 inches or 8 inches would make the triangle meet this criterion. Also, since 6 inches and 8 inches are equal to 
Example Question #71 : Geometry
Which is the greater quantity?
(a)
(b)
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) and (b) are equal.
A triangle must have at least two acute angles; if 
Example Question #2 : Isosceles Triangles
Note: Figure NOT drawn to scale.
Refer to the above diagram. Which expression is equivalent to 
The correct answer is not among the other choices.
This is an isosceles triangle, so the left and right sides are of equal length. Draw the altitude of this triangle, as follows:
The altitude is a perpendicular bisector of the base; it is one leg of a right triangle with half the base, which is 15 inches, as the other leg, and one side, which is 
Example Question #3 : Isosceles Triangles
Note: Figure NOT drawn to scale.
Which of the following is the greater quantity?
(A) The perimeter of the triangle
(B) 90
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
The longest side of the triangle appears opposite the angle of greatest measure. The side of length 30 appears opposite an angle of measure 
If we let this common length be 
The perimeter of the triangle is therefore greater than 90.
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