Triangle Congruence Theorems Flashcard

Front

In the figure shown, which theorem can be used to show that △ABC ≅ △DEF?

Back

ASA Triangle Congruence Theorem

Answer explanation

The ASA Triangle Congruence Theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. This applies to △ABC and △DEF.

Front

Which theorem is not a valid theorem to show that two triangles are congruent? Options: SAS Triangle Congruence Theorem, SSA Triangle Congruence Theorem, ASA Triangle Congruence Theorem, AAS Triangle Congruence Theorem.

Back

SSA Triangle Congruence Theorem.

Answer explanation

The SSA Triangle Congruence Theorem is not valid for proving triangle congruence because it can lead to ambiguous cases, unlike SAS, ASA, and AAS, which reliably establish congruence.

Front

In the figure shown, what additional information is needed to show that △ABC ≅ △DEF by ASA? Options: Measure of angle A, Length of side BC, Measure of angle C, Length of side AB.

Back

Measure of angle C.

Answer explanation

To show that △ABC ≅ △DEF by ASA, we need two angles and the included side. Knowing the measure of angle C allows us to establish the necessary angle relationships, making it the correct choice.

Front

Which pair of triangles is congruent by ASA? Select all that apply. Options: Pair A, Pair B, Pair C, Pair D.

Back

Pair A.

Answer explanation

Pair A is congruent by ASA (Angle-Side-Angle) because it has two angles and the included side equal to the corresponding parts of another triangle. The other pairs do not meet the ASA criteria.

Front

In the figure shown, what is the value of x? Options: 2, 3, 4, 5

Back

4

Answer explanation

To find the value of x, we analyze the figure and apply the relevant mathematical principles. The calculations lead us to conclude that x equals 4, making it the correct choice among the options provided.

Front

In the figure shown, what is the measure of angle B if △ABC ≅ △DEF by ASA? Options: 45°, 60°, 90°, 75°.

Back

60°.

Front

What is necessary to prove △GHI ≅ △JKL using the SAS Triangle Congruence Theorem?

Back

The length of side GH

Front

In the figure shown, if △XYZ ≅ △PQR by AAS, what is the length of side YZ? Options: 5 cm, 6 cm, 7 cm, 8 cm.

Back

7 cm.