Geometry Congruent Triangles and Rigid Motions Test with Point Values (PDF)

Geometry math test: Congruent Triangles and Rigid Motions – Maths PDF

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This congruence test for Geometry covers congruent triangles and rigid motions (Common Core G-CO.B.7, G-CO.B.8), with a free PDF to print.

This 45-minute test checks congruence by rigid motions and the triangle congruence tests. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Congruent Triangles and Rigid Motions
Standards: G-CO.B.7, G-CO.B.8
Time: 45 minutes
Total: 20 points

Congruence test: questions

Question 1 – Corresponding parts [2 pts]

Triangle ABC is congruent to triangle DEF.

The triangles are congruent with vertices matching in order. Find \(x\) and \(m\angle D\).

Question 2 – Which test? [3 pts]

Triangles with AB = DE, BC = EF and AC = DF. (1 point)
Triangles with AB = DE, m∠A = m∠D and AC = DF. (1 point)
Triangles with AB = DE, BC = EF and m∠A = m∠D, where angle A is opposite BC. (1 point)

Question 3 – Congruence by coordinates [2 pts]

Triangle ABC and its image under (x + 6, y + 1).

Triangle ABC has A(0, 0), B(6, 0) and C(2, 3). Under a translation, A maps to D(6, 1). Find E and F, and explain why the triangles are congruent.

Question 4 – Proof with a shared side [3 pts]

AB = AD and CB = CD.

In kite ABCD, AB = AD and CB = CD. Prove that \(\angle B\) and \(\angle D\) are congruent. Give each statement with a reason.

Question 5 – Hypotenuse-leg [2 pts]

Two right triangles each have a hypotenuse of 17 and one leg of 8. Show that they are congruent, and find the area of each.

Question 6 – SSA counterexample [2 pts]

Explain with a sketch or numbers why two triangles with sides 5 and 8 and a 30° angle opposite the side of length 5 are not necessarily congruent.

Question 7 – Third angle [2 pts]

Triangle ABC has m∠A = 40°, m∠B = 75° and AB = 11. Triangle DEF has m∠D = 40°, m∠F = 65° and DE = 11. Are the triangles congruent? Justify.

Question 8 – Surveying [2 pts]

Two surveyors stand 24 yards apart at points A and B on one side of a pond. Each measures the angle to a rock R across the pond as 52° at A and 61° at B. A third surveyor does the same from points C and D, also 24 yards apart, with 52° at C and 61° at D. Are the distances AR and the matching distance from C equal? Which test applies?

Question 9 – Perimeter [2 pts]

Triangle PQR is congruent to triangle XYZ with PQ = 2n + 1, XY = 3n – 4 and QR = 14. Find n and the perimeter of XYZ if PR = 9.

Key facts behind this congruence test

Key facts

Congruent triangles have three pairs of congruent sides and three pairs of congruent angles.
Valid tests: SSS, SAS, ASA, AAS and, for right triangles, HL.
SSA and AAA do not prove congruence.
CPCTC: after proving triangles congruent, corresponding parts are congruent.
A rigid motion maps a figure onto a congruent figure.

How to use this congruence test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

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