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.
Concepts
A triangle has side lengths 6, 8, and 11. Which of the following best
classifies the triangle?
Which of the following sets of side lengths forms a right triangle?
Procedures
A right triangle has a hypotenuse of length 17 and one leg of
length 8. What is the length of the other leg?
Triangles ABC and DEF are similar with AB corresponding to DE.
AB = 6, BC = 9, and DE = 10. What is the length of EF?
A circle has a diameter of 14. What is the area of the circle, in
terms of pi?
What is the distance between the points (-2, 3) and (6, 9) in the
coordinate plane?
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?
A rectangular prism (box) has dimensions 4 by 5 by 6. What is its
volume?
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?
Applications
Two similar triangles have corresponding side lengths in the ratio
2 : 3. The smaller triangle has an area of 20 square inches. What
is the area of the larger triangle, in square inches?
A circular running track has a circumference of 400 meters. To the
nearest meter, what is the radius of the track? (Use pi ~= 3.14.)
In triangle ABC, AB = 5, AC = 7, and angle A = 60 degrees. What is
the length of side BC?