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ACT Geometry — Tutor Intake Assessment

This is a spot-check intake covering the highest-leverage ACT geometry skills. The goal is to surface where your understanding breaks down so we can plan the next several sessions — not to grade you. Work the problems as you would on the ACT (no formula sheet). If you don't see how to start a problem, move on and we'll discuss it together.

Grade 10·12 problems·~15 min·ACT Math·category·act-geo
Work through problems with immediate feedback
A

Concepts

1.

A triangle has side lengths 6, 8, and 11. Which of the following best
classifies the triangle?

2.

Which of the following sets of side lengths forms a right triangle?

B

Procedures

1.

A right triangle has a hypotenuse of length 17 and one leg of
length 8. What is the length of the other leg?

2.

Triangles ABC and DEF are similar with AB corresponding to DE.
AB = 6, BC = 9, and DE = 10. What is the length of EF?

3.

A circle has a diameter of 14. What is the area of the circle, in
terms of pi?

4.

What is the distance between the points (-2, 3) and (6, 9) in the
coordinate plane?

5.

A triangle has a base of 12 and a perpendicular height of 5 from
that base to the opposite vertex. What is the area of the
triangle?

6.

A rectangular prism (box) has dimensions 4 by 5 by 6. What is its
volume?

7.

In a right triangle, the angle theta is acute. The side opposite
theta has length 5 and the hypotenuse has length 13. What is the
length of the side adjacent to theta?

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