Congruent Triangles Test – Geometry Math (Printable PDF)

Question 1 Corresponding parts with algebra (2 points)

△ABC ≅ △DEF.

1. AB = 4x − 3 and DE = 2x + 9. Find DE. (1 point)
2. m∠C = (7y − 6)° and m∠F = (4y + 18)°. Find m∠F. (1 point)

Question 2 Choose the criterion (3 points)

For each set of givens about △ABC and △DEF, name the criterion that proves congruence, or write “none.”

1. AB ≅ DE, ∠B ≅ ∠E, BC ≅ EF (1 point)
2. ∠A ≅ ∠D, AC ≅ DF, ∠C ≅ ∠F (1 point)
3. AB ≅ DE, BC ≅ EF, ∠A ≅ ∠D (1 point)

Question 3 Right triangles (3 points)

Right triangles ABC and DEF have right angles at B and E, hypotenuses AC = DF = 15, and legs AB = DE = 9.

1. Name the criterion that proves the triangles congruent. (1 point)
2. Find BC. (1 point)
3. Find the area of △DEF. (1 point)

Question 4 Prove with SAS (3 points)

Given: AB ∥ DC and AB ≅ DC. Prove: △ABC ≅ △CDA.

Question 5 Congruence on the plane (3 points)

△RST has R(0, 0), S(6, 0) and T(6, 8). △UVW has U(1, 1), V(1, 7) and W(9, 7). Show that the triangles are congruent.

Question 6 Why SSA fails (2 points)

Two triangles each have sides of 7 and 10 and a 35° angle that is not between them. Must the triangles be congruent? Explain.

Question 7 Truss beams (2 points)

A roof truss uses congruent triangles △ABC ≅ △DEF. AB = 3.5 m, BC = 4.2 m and CA = 5.6 m. Find DF. Beams cost $12.50 per meter. What is the cost of the beams for both triangles?

Question 8 Paragraph proof with ASA (2 points)

Given: BD bisects ∠ABC and ∠ADC. Prove: AB ≅ CB. Write a short paragraph proof.