Congruent Triangles
A free Geometry lesson from the “Triangles, Similarity, and Trigonometry” unit, with a worked example and practice problems including step-by-step solutions.
Congruent triangles have the same size and shape, which means corresponding sides and corresponding angles are equal. Triangle congruence shortcuts, such as SSS, SAS, ASA, and AAS, let you prove triangles are congruent without checking all six parts. This matters because once triangles are proven congruent, you can use corresponding parts to solve for missing measures. When practicing, match vertices in the correct order and identify which sides or angles correspond. A common mistake is assuming triangles are congruent from appearance alone instead of using a valid congruence reason.
What you'll learn
- Match corresponding parts
- Use congruence statements
- Find missing measures
Worked example
Problem. Triangles ABC and DEF are congruent in that order. If AB = 9, what is DE?
- The order ABC matches DEF.
- Side AB corresponds to side DE.
- Corresponding sides are equal.
- Connect the result back to Congruent Triangles so the geometric relationship is explicit.
Answer: 9
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Congruent triangles have...
Choices: Equal corresponding sides and angles · Only equal areas · Only equal perimeters · No matching parts
Show solution
- Congruence preserves side lengths and angle measures.
Answer: Equal corresponding sides and angles
2. Triangles ABC and DEF are congruent. If angle A is 40 degrees, what is angle D?
Show solution
- A corresponds to D.
Answer: 40
3. Triangles ABC and DEF are congruent. If BC = 12, what is EF?
Show solution
- BC corresponds to EF.
Answer: 12
4. If triangle CAT is congruent to triangle DOG, side CA corresponds to...
Choices: DO · OG · DG · GO
Show solution
- C matches D and A matches O.
Answer: DO
5. Corresponding sides are 3x and 24. Find x.
Show solution
- 3x = 24.
Answer: 8
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