Triangles

Practice Questions

ISEE Upper Level (grades 9-12) Quantitative Reasoning › Triangles

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1

The lengths of the hypotenuses of ten similar right triangles form an arithmetic sequence. The smallest triangle has legs of lengths 5 and 12 inches; the second-smallest triangle has a hypotenuse of length one and one half feet.

Which of the following responses comes closest to the area of the largest triangle?

2

Which is the greater quantity?

(a) The sum of the measures of the exterior angles of a thirty-sided polygon, one per vertex

(b) The sum of the measures of the exterior angles of a forty-sided polygon, one per vertex

3

In a certain quadrilateral, three of the angles are , , and . What is the measure of the fourth angle?

4

and are right triangles, with right angles , respectively.

Which is the greater quantity?

(a) The perimeter of

(b) The perimeter of

5

A rectangle is two feet longer than it is wide; its perimeter is 11 feet. What is its area in square inches?

6

Trapezoid

Figure NOT drawn to scale.

In the above figure, is the midsegment of isosceles Trapezoid . Also, .

What is the perimeter of Trapezoid ?

7

Given Trapezoid , where . Also,

Which is the greater quantity?

(a)

(b)

8

and are right triangles, with right angles , respectively. and .

Which is the greater quantity?

(a)

(b)

9

The lengths of the hypotenuses of ten similar right triangles form an arithmetic sequence. The smallest triangle has legs of lengths 5 and 12 inches; the second-smallest triangle has a hypotenuse of length one and one half feet.

Which of the following responses comes closest to the area of the largest triangle?

10

Trapezoid

The above diagram depicts trapezoid . Which is the greater quantity?

(a)

(b)

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