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Triangle Congruence: SSS, SAS, ASA, AAS & HL — Easy Worksheet 1
Grade 10 · Whoobee Name: ____________________ Date: __________
Matching tick marks show congruent sides and matching arcs show congruent angles. Write SSS, SAS, ASA, AAS or HL, or write none if the marked parts do not prove the triangles congruent.
How to solve
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Example
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
Answer: ASA
Not quite. The answer is
💡 Two pairs of angles are marked, ∠A ≅ ∠D and ∠B ≅ ∠E, and so is the side between them, AB ≅ DE. Two angles and the included side is ASA.
✓ Correct!
Not quite. The answer is
💡 Two pairs of angles are marked, ∠A ≅ ∠D and ∠B ≅ ∠E, and so is the side between them, AB ≅ DE. Two angles and the included side is ASA.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 All three pairs of sides are marked: AB ≅ DE, BC ≅ EF and AC ≅ DF. Three pairs of congruent sides is SSS.
✓ Correct!
Not quite. The answer is
💡 All three pairs of sides are marked: AB ≅ DE, BC ≅ EF and AC ≅ DF. Three pairs of congruent sides is SSS.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two pairs of sides are marked, AB ≅ DE and BC ≅ EF, and so is the angle between them, ∠B ≅ ∠E. Two sides and the included angle is SAS.
✓ Correct!
Not quite. The answer is
💡 Two pairs of sides are marked, AB ≅ DE and BC ≅ EF, and so is the angle between them, ∠B ≅ ∠E. Two sides and the included angle is SAS.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two pairs of angles are marked, ∠C ≅ ∠F and ∠A ≅ ∠D, and so is the side between them, AC ≅ DF. Two angles and the included side is ASA.
✓ Correct!
Not quite. The answer is
💡 Two pairs of angles are marked, ∠C ≅ ∠F and ∠A ≅ ∠D, and so is the side between them, AC ≅ DF. Two angles and the included side is ASA.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two pairs of sides are marked, BC ≅ EF and AC ≅ DF, and so is the angle between them, ∠C ≅ ∠F. Two sides and the included angle is SAS.
✓ Correct!
Not quite. The answer is
💡 Two pairs of sides are marked, BC ≅ EF and AC ≅ DF, and so is the angle between them, ∠C ≅ ∠F. Two sides and the included angle is SAS.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 All three pairs of sides are marked: AB ≅ DE, BC ≅ EF and AC ≅ DF. Three pairs of congruent sides is SSS.
✓ Correct!
Not quite. The answer is
💡 All three pairs of sides are marked: AB ≅ DE, BC ≅ EF and AC ≅ DF. Three pairs of congruent sides is SSS.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two pairs of angles are marked, ∠B ≅ ∠E and ∠C ≅ ∠F, and so is the side between them, BC ≅ EF. Two angles and the included side is ASA.
✓ Correct!
Not quite. The answer is
💡 Two pairs of angles are marked, ∠B ≅ ∠E and ∠C ≅ ∠F, and so is the side between them, BC ≅ EF. Two angles and the included side is ASA.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Two pairs of sides are marked, AC ≅ DF and AB ≅ DE, and so is the angle between them, ∠A ≅ ∠D. Two sides and the included angle is SAS.
✓ Correct!
Not quite. The answer is
💡 Two pairs of sides are marked, AC ≅ DF and AB ≅ DE, and so is the angle between them, ∠A ≅ ∠D. Two sides and the included angle is SAS.
💡 How to solve: Triangle Congruence: SSS, SAS, ASA, AAS & HL
List what is marked congruent, in order around the triangle. Three sides is SSS. Two sides and the angle between them is SAS. Two angles and the side between them is ASA; two angles and a side not between them is AAS. In right triangles, a hypotenuse and a leg is HL. Two sides and a non-included angle (SSA) or three angles (AAA) prove nothing, so the answer is none.
Try a similar one
Which postulate or theorem, if any, proves △ABC ≅ △DEF? (SSS, SAS, ASA, AAS, HL, or none)
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Triangle Congruence: SSS, SAS, ASA, AAS & HL — Easy Worksheet 1
Matching tick marks show congruent sides and matching arcs show congruent angles. Write SSS, SAS, ASA, AAS or HL, or write none if the marked parts do not prove the triangles congruent.