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Congruent Triangles and Corresponding Parts Quiz

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Which of the following is NOT a congruence criterion for triangles?

Angle-Angle-Side (AAS)

Explanation

AAS is not a congruence criterion; it's ambiguous for proving triangle congruence.

Which of the following is a postulate commonly used to prove congruence of two triangles?

Angle-Side-Angle (ASA) Postulate

Explanation

ASA postulate 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.

Which congruence criterion involves showing that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle?

Side-Angle-Side (SAS)

Explanation

SAS criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another, then the triangles are congruent.

Which congruence criterion involves showing that two angles and the included side of one triangle are congruent to two angles and the included side of another triangle?

Angle-Angle-Side (AAS)

Explanation

AAS criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another, then the triangles are congruent.

Which congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent?

Angle-Side-Angle (ASA)

Explanation

ASA states that triangles are congruent if two angles and the included side are equal.

If two triangles are congruent, what can be said about their corresponding angles and sides?

All corresponding sides are equal, but corresponding angles may not be equal.

Explanation

Congruent triangles have equal corresponding sides, but angles may vary.

If two triangles have corresponding sides of equal length, which congruence criterion can be used to prove that the triangles are congruent?

Side-Side-Side (SSS)

Explanation

SSS criterion states that if all three sides of one triangle are equal to the corresponding sides of another, the triangles are congruent.

What is the minimum number of pieces of information required to prove two triangles congruent using the Side-Side-Side (SSS) congruence criterion?

Three sides

Explanation

Three corresponding sides must be given for SSS to prove triangle congruence.

If two triangles are congruent, what can be said about their corresponding medians?

Corresponding medians are equal in length.

Explanation

Congruent triangles have corresponding medians with equal lengths.

#10

In triangle ABC and triangle DEF, if angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F, which congruence criterion can be applied?

Angle-Angle-Angle (AAA)

Explanation

AAA criterion applies when all three angles of one triangle are congruent to the corresponding angles of another.

#11

In triangle XYZ and triangle PQR, if XY is congruent to PQ, YZ is congruent to QR, and XZ is congruent to PR, which congruence criterion can be applied?

Side-Side-Side (SSS)

Explanation

SSS criterion applies when all three sides of one triangle are congruent to the corresponding sides of another.

#12

If triangle ABC is congruent to triangle DEF under the Angle-Angle-Side (AAS) criterion, and angle A is congruent to angle D, angle B is congruent to angle E, and side AC is congruent to side DF, what can be concluded about angle C and angle F?

Angle C is congruent to angle F.

Explanation

The third angle is congruent when two triangles are congruent under AAS.

#13

If triangle PQR is congruent to triangle STU under the Side-Side-Side (SSS) criterion, and PQ is congruent to ST, QR is congruent to TU, and PR is congruent to SU, what can be concluded about angle Q and angle U?

Insufficient information to determine.

Explanation

SSS criterion only verifies side lengths, not angles.

#14

If triangle ABC is congruent to triangle DEF under the Angle-Side-Angle (ASA) criterion, and angle A is congruent to angle D, side BC is congruent to side EF, and angle C is congruent to angle F, what can be concluded about side AB and side DE?

Side AB is congruent to side DE.

Explanation

ASA criterion establishes that if two angles and the included side of one triangle are congruent to two angles and the included side of another, then the triangles are congruent.

Congruent Triangles and Corresponding Parts Quiz

Which of the following is NOT a congruence criterion for triangles?

Which of the following is a postulate commonly used to prove congruence of two triangles?

Which congruence criterion involves showing that two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle?

Which congruence criterion involves showing that two angles and the included side of one triangle are congruent to two angles and the included side of another triangle?

Which congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent?

If two triangles are congruent, what can be said about their corresponding angles and sides?

If two triangles have corresponding sides of equal length, which congruence criterion can be used to prove that the triangles are congruent?

What is the minimum number of pieces of information required to prove two triangles congruent using the Side-Side-Side (SSS) congruence criterion?

If two triangles are congruent, what can be said about their corresponding medians?

In triangle ABC and triangle DEF, if angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F, which congruence criterion can be applied?

In triangle XYZ and triangle PQR, if XY is congruent to PQ, YZ is congruent to QR, and XZ is congruent to PR, which congruence criterion can be applied?

If triangle ABC is congruent to triangle DEF under the Angle-Angle-Side (AAS) criterion, and angle A is congruent to angle D, angle B is congruent to angle E, and side AC is congruent to side DF, what can be concluded about angle C and angle F?

If triangle PQR is congruent to triangle STU under the Side-Side-Side (SSS) criterion, and PQ is congruent to ST, QR is congruent to TU, and PR is congruent to SU, what can be concluded about angle Q and angle U?

If triangle ABC is congruent to triangle DEF under the Angle-Side-Angle (ASA) criterion, and angle A is congruent to angle D, side BC is congruent to side EF, and angle C is congruent to angle F, what can be concluded about side AB and side DE?

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