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GEO.21 Use indirect reasoning in geometry Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.21 Use indirect reasoning in geometry. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.21 Use indirect reasoning in geometry - High school geometry skill focused on indirect reasoning in geometry.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.21 Use indirect reasoning in geometry skill assessments:

Problem 1Difficulty: Mastery

Which statement is the contrapositive of: “If two triangles are similar, then corresponding angles are congruent”?

AIf corresponding angles are congruent, then the triangles are similar.

BIf the triangles are not similar, then corresponding angles are not congruent.

CIf two triangles are similar, then corresponding sides are equal.

DIf a pair of corresponding angles are not congruent, then the triangles are not similar.

Solution & Explanation:Contrapositive reverses and negates: similar ⇒ corresponding angles congruent becomes (corresponding angles not congruent) ⇒ (not similar).

Problem 2Difficulty: Mastery

A student claims there is a triangle with angles measuring 95°, 60°, and 40°. Use indirect reasoning to show the claim is false. Which assumption and contradiction are valid?

AAssume such a triangle exists; then the angle sum would be 95° + 60° + 40° = 195°, contradicting the Triangle Sum Theorem (sum must be 180°).

BAssume no such triangle exists; then claim 95° + 60° + 40° = 180°, contradicting arithmetic but starting with the wrong assumption.

CAssume the triangle is right; then one angle is 90°, which is unrelated.

DAssume the triangle is isosceles; then two angles are equal, which does not address the sum.

Solution & Explanation:Triangle angles must sum to 180°. The proposed angles sum to 195°, so assuming the triangle exists contradicts the Triangle Sum Theorem.

Problem 3Difficulty: Mastery

In triangle ABC, points D on AB and E on AC satisfy AD = 3, DB = 6, AE = 4, and EC = 8. You want to prove DE ∥ BC using an indirect proof. Which assumption and contradiction are correct?

AAssume DE ∥ BC; then claim AD is not one-third of AB, contradicting arithmetic but starting with the wrong assumption.

BAssume D is the midpoint of AB; then DE ∥ BC, which is false here because AD ≠ DB.

CAssume DE is not parallel to BC; then triangles ADE and ABC would not have a consistent scale factor along both sides. But AD and AE are each one-third of their full sides (since 3 is one-third of 9 and 4 is one-third of 12), which forces similarity and thus DE ∥ BC, a contradiction.

DAssume ∠A is 45°; then DE ∥ BC, which is unrelated.

Solution & Explanation:Both sides are divided in the same ratio: AD is one-third of AB and AE is one-third of AC. That forces triangles ADE and ABC to be similar, so DE must be parallel to BC. Assuming it is not parallel contradicts the forced similarity.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard GEO.21 (High school geometry skill focused on indirect reasoning in geometry.).