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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. In Coordinate Geometry and Proof, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.

What you'll learn

Worked example

Problem. Find the midpoint of (2, 8) and (10, 4).

  1. Average x-values: (2 + 10)/2 = 6.
  2. Average y-values: (8 + 4)/2 = 6.
  3. The midpoint is (6, 6).
  4. Connect the result back to Geometry Readiness Test so the geometric relationship is explicit.

Answer: (6, 6)

Practice problems

1. An angle is supplementary to 136 degrees. What is its measure?

Show solution
  1. Course Review: First identify exactly what the question is asking: An angle is supplementary to 136 degrees. What is its measure?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. 180 - 136 = 44.
  4. Check the result by substituting or estimating: the response should match 44 and make sense in the original problem.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: 44

2. A triangle has angles 48 and 57 degrees. Find the third angle.

Show solution
  1. Course Review: First identify exactly what the question is asking: A triangle has angles 48 and 57 degrees. Find the third angle.
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. 180 - 105 = 75.
  4. Check the result by substituting or estimating: the response should match 75 and make sense in the original problem.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: 75

3. Same-side interior angles include 112 degrees. What is the other angle?

Show solution
  1. Course Review: First identify exactly what the question is asking: Same-side interior angles include 112 degrees. What is the other angle?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. 180 - 112 = 68.
  4. Check the result by substituting or estimating: the response should match 68 and make sense in the original problem.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: 68

4. Which shortcut uses two angles and a non-included side?

Choices: AAS · SAS · SSS · HL

Show solution
  1. Course Review: First identify exactly what the question is asking: Which shortcut uses two angles and a non-included side?
  2. Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
  3. Angle-angle-side.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: AAS

5. A side of 8 scales by factor 2.5. What is the new length?

Show solution
  1. Course Review: First identify exactly what the question is asking: A side of 8 scales by factor 2.5. What is the new length?
  2. Use the structure of the expression to choose a factoring pattern, then check that the factors multiply back to the original expression.
  3. 8 x 2.5 = 20.
  4. Check the result by substituting or estimating: the response should match 20 and make sense in the original problem.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: 20

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