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Congruent Triangles - Worksheet 7 - 10th Grade

Medium

Prove triangle congruence using congruence criteria (Medium)

18 problems · 25-30 minutes · Skills: triangles, congruence, proofs

About This Worksheet

This medium-level worksheet contains 18 problems designed for 10th Grade students practicing congruent triangles. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Triangle congruence is the engine behind a huge portion of geometric proof. From proving that diagonals of a parallelogram bisect each other to establishing properties of isosceles triangles, CPCTC and the congruence criteria are used repeatedly throughout the course and in subsequent math courses.

  • Apply SSS, SAS, ASA, AAS, and HL congruence criteria to determine if triangles are congruent
  • Write two-column proofs to prove triangle congruence
  • Use CPCTC to conclude that corresponding parts of congruent triangles are congruent
  • Write correct congruence statements matching corresponding vertices in order
  • Identify which congruence criterion applies given marked diagrams or listed information

How to Solve: Worked Example

Example Problem: Two angles and a non-included side are congruent. Which theorem applies?
Solution Steps:
  1. Two angles and a side are given.
  2. The side is not between the two angles, so it is not ASA.
  3. The correct theorem is AAS.
Answer: AAS
Tip: ASA has the side between the angles; AAS has it outside. The position is what distinguishes them.
1
Are all congruent triangles also similar?
2
HL applies only to which kind of triangle?
3
In SAS, where must the angle be?
4
Do congruent triangles have equal area?
5
What abbreviation states that corresponding parts of congruent triangles are congruent?
6
In ASA, where must the side be?
7
What does the S stand for in SSS?
8
What does the A stand for in ASA?
9
Three pairs of congruent sides. Which postulate proves congruence?
10
Two sides and the included angle. Which postulate?
11
Right triangles with congruent hypotenuse and one leg. Which theorem?
12
Congruent triangles have congruent corresponding what?
13
Two angles and the included side. Which postulate?
14
Two angles and a non-included side. Which theorem?
15
Are all congruent triangles also similar?
16
HL applies only to which kind of triangle?
17
In SAS, where must the angle be?
18
Do congruent triangles have equal area?

Answer Key

1. Yes2. right triangles3. between the two sides4. Yes5. CPCTC6. between the two angles7. side8. angle9. SSS10. SAS11. HL12. sides and angles13. ASA14. AAS15. Yes16. right triangles17. between the two sides18. Yes

Frequently Asked Questions

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Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

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What skills does this triangles worksheet cover?

This worksheet focuses on triangles, congruence, proofs. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.