Geometry Readiness Test
A free Geometry lesson from the “Coordinate Geometry and Proof” unit, with a worked example and practice problems including step-by-step solutions.
The Geometry readiness test samples angles, triangles, congruence, similarity, right triangles, measurement, circles, transformations, coordinate geometry, and proof reasoning.
What you'll learn
- Demonstrate Geometry readiness
- Use mixed geometry strategies
- Prepare for proof and coordinate work
Worked example
Problem. Find the midpoint of (2, 8) and (10, 4).
- Average x-values: (2 + 10)/2 = 6.
- Average y-values: (8 + 4)/2 = 6.
- The midpoint is (6, 6).
Answer: (6, 6)
Practice problems
1. An angle is supplementary to 136 degrees. What is its measure?
Show solution
- Course Review: First identify exactly what the question is asking: An angle is supplementary to 136 degrees. What is its measure?
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- 180 - 136 = 44.
- Check the result by substituting or estimating: the response should match 44 and make sense in the original problem.
Answer: 44
2. A triangle has angles 48 and 57 degrees. Find the third angle.
Show solution
- Course Review: First identify exactly what the question is asking: A triangle has angles 48 and 57 degrees. Find the third angle.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- 180 - 105 = 75.
- Check the result by substituting or estimating: the response should match 75 and make sense in the original problem.
Answer: 75
3. Same-side interior angles include 112 degrees. What is the other angle?
Show solution
- Course Review: First identify exactly what the question is asking: Same-side interior angles include 112 degrees. What is the other angle?
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- 180 - 112 = 68.
- Check the result by substituting or estimating: the response should match 68 and make sense in the original problem.
Answer: 68
4. Which shortcut uses two angles and a non-included side?
Choices: AAS · SAS · SSS · HL
Show solution
- Course Review: First identify exactly what the question is asking: Which shortcut uses two angles and a non-included side?
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Angle-angle-side.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: AAS
5. A side of 8 scales by factor 2.5. What is the new length?
Show solution
- Course Review: First identify exactly what the question is asking: A side of 8 scales by factor 2.5. What is the new length?
- Use the structure of the expression to choose a factoring pattern, then check that the factors multiply back to the original expression.
- 8 x 2.5 = 20.
- Check the result by substituting or estimating: the response should match 20 and make sense in the original problem.
Answer: 20
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