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Proving Angles Congruent and Angle Relationships Quiz

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In a right triangle, what is the name of the angle opposite the hypotenuse?

Obtuse angle

Explanation

The angle opposite the hypotenuse in a right triangle is called an obtuse angle.

If two angles are complementary, what is their sum?

90 degrees

Explanation

The sum of two complementary angles is always 90 degrees.

In a parallelogram, what can you conclude about consecutive angles?

They are supplementary

Explanation

Consecutive angles in a parallelogram are supplementary.

If m∠A = 60° and m∠B = 120°, what is the measure of ∠C in triangle ABC?

30 degrees

Explanation

The measure of angle C in triangle ABC is 30 degrees.

If two angles are congruent and supplementary, what can you conclude about their measures?

They are both straight angles

Explanation

Congruent and supplementary angles have measures totaling 180 degrees, forming straight angles.

What is the congruence statement for two vertical angles?

∠A ≅ ∠C

Explanation

The congruence statement for two vertical angles is ∠A ≅ ∠C.

Which of the following is NOT a valid method to prove two triangles congruent?

AAA (Angle-Angle-Angle) Congruence Postulate

Explanation

AAA (Angle-Angle-Angle) is not a valid method to prove two triangles congruent.

Which theorem states that if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent?

ASA (Angle-Side-Angle) Congruence Theorem

Explanation

ASA (Angle-Side-Angle) Congruence Theorem states the conditions for triangle congruence.

If two angles form a linear pair, what can you conclude about their sum?

Their sum is 180 degrees

Explanation

The sum of two angles forming a linear pair is always 180 degrees.

#10

Which congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent?

SAS (Side-Angle-Side) Congruence Theorem

Explanation

SAS (Side-Angle-Side) Congruence Theorem establishes conditions for triangle congruence.

#11

In triangle ABC, if ∠A ≅ ∠C, which congruence postulate can be used to prove triangle ABC congruent to triangle DEF?

AAS (Angle-Angle-Side) Congruence Postulate

Explanation

If two angles and one side are congruent in two triangles, AAS Congruence Postulate can be applied.

#12

If in triangle ABC, side AB is congruent to side DE, side AC is congruent to side DF, and angle A is congruent to angle D, which congruence postulate can be used to prove triangle ABC congruent to triangle DEF?

SAS (Side-Angle-Side) Congruence Postulate

Explanation

If two sides and the included angle are congruent in two triangles, SAS Congruence Postulate can be applied.

#13

In triangle XYZ, if side XY is congruent to side MN, side XZ is congruent to side MP, and angle X is congruent to angle M, which congruence postulate can be used to prove triangle XYZ congruent to triangle MNP?

SAS (Side-Angle-Side) Congruence Postulate

Explanation

If two sides and the included angle are congruent in two triangles, SAS Congruence Postulate can be applied.

#14

In triangle DEF, if side DE is congruent to side JK, side EF is congruent to side KL, and side DF is congruent to side JL, which congruence postulate can be used to prove triangle DEF congruent to triangle JKL?

SSS (Side-Side-Side) Congruence Postulate

Explanation

If all three sides are congruent in two triangles, SSS Congruence Postulate can be applied.

#15

In triangle PQR, if side PQ is congruent to side RS, side PR is congruent to side RT, and side QR is congruent to side ST, which congruence postulate can be used to prove triangle PQR congruent to triangle RST?

SSS (Side-Side-Side) Congruence Postulate

Explanation

If all three sides are congruent in two triangles, SSS Congruence Postulate can be applied.

Proving Angles Congruent and Angle Relationships Quiz

In a right triangle, what is the name of the angle opposite the hypotenuse?

If two angles are complementary, what is their sum?

In a parallelogram, what can you conclude about consecutive angles?

If m∠A = 60° and m∠B = 120°, what is the measure of ∠C in triangle ABC?

If two angles are congruent and supplementary, what can you conclude about their measures?

What is the congruence statement for two vertical angles?

Which of the following is NOT a valid method to prove two triangles congruent?

Which theorem states that if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent?

If two angles form a linear pair, what can you conclude about their sum?

Which congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent?

In triangle ABC, if ∠A ≅ ∠C, which congruence postulate can be used to prove triangle ABC congruent to triangle DEF?

If in triangle ABC, side AB is congruent to side DE, side AC is congruent to side DF, and angle A is congruent to angle D, which congruence postulate can be used to prove triangle ABC congruent to triangle DEF?

In triangle XYZ, if side XY is congruent to side MN, side XZ is congruent to side MP, and angle X is congruent to angle M, which congruence postulate can be used to prove triangle XYZ congruent to triangle MNP?

In triangle DEF, if side DE is congruent to side JK, side EF is congruent to side KL, and side DF is congruent to side JL, which congruence postulate can be used to prove triangle DEF congruent to triangle JKL?

In triangle PQR, if side PQ is congruent to side RS, side PR is congruent to side RT, and side QR is congruent to side ST, which congruence postulate can be used to prove triangle PQR congruent to triangle RST?

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