Step: 1

: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

[SSS postulate.]

Step: 2

In the given triangles, three sides of first triangle are congruent to the corresponding three sides of second triangle.

Step: 3

So, ΔABC ≅ ΔPQR by the SSS congruence condition.

Correct Answer is : ΔABC ≅ ΔPQR (SSS Congruence Rule/Criterion )

Step: 1

[Given.]

Step: 2

[Reflexive property of congruence.]

Step: 3

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.

[SAS Postulate.]

Step: 4

If ∠ABD = ∠CBD, then by the SAS Postulate, ΔADB ≅ ΔCDB.

Correct Answer is : ∠ABD = ∠CBD

Step: 1

[Given.]

Step: 2

[Given.]

Step: 3

∠ACB = ∠EDC

[Vertical angles are congruent.]

Step: 4

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.

Step: 5

Thererfore, ΔABC ≅ ΔEDC by using SAS postulate.

Correct Answer is : SAS postulate

Step: 1

[Given.]

Step: 2

[Given.]

Step: 3

[Reflexive property of congruence.]

Step: 4

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step: 5

Therefore, ΔABD ≅ ΔCBD by using SSS postulate.

Correct Answer is : SSS postulate

Step: 1

If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the two triangles are congruent.

Step: 2

As QR ¯ ≅ TR ¯ , PQ ¯ ≅ ST ¯ and ∠PQR = ∠STR, by SAS theorem, we have ΔRQP ≅ ΔRTS.

Correct Answer is : SAS postulate

Step: 1

[Given.]

Step: 2

∠PRQ = ∠SRT

[Vertical angles congruent.]

Step: 3

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.

Step: 4

If QR ¯ ≅ TR ¯ , then by the SAS Postulate, ΔQRP ≅ ΔTRS.

Correct Answer is : QR ¯ ≅ TR ¯

Step: 1

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

[SSS Postulate.]

Step: 2

As AB ¯ ≅ CB ¯ , AD ¯ ≅ CD ¯ and BD ¯ ≅ BD ¯ , by SSS theorem, we have ΔBAD ≅ΔBCD.

Correct Answer is : SSS postulate

Step: 1

[Given.]

Step: 2

[Reflexive property of congruence.]

Step: 3

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

[SSS Postulate.]

Step: 4

If PS ¯ ≅ RQ ¯ , then by the SSS postulate, ΔPQS ≅ΔRSQ.

Correct Answer is : PS ¯ ≅ QR ¯

Step: 1

[Given.]

Step: 2

∠ABC = ∠ZYX

[Given.]

Step: 3

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.

Step: 4

If AB ¯ ≅ ZY ¯ , then by the SAS Postulate, ΔABC ≅ ΔZYX.

Correct Answer is : AB ¯ ≅ ZY ¯

Step: 1

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent

[SAS postulate.]

Step: 2

In Figure 3, two sides and the included angle of first triangle are congruent to the corresponding two sides and the included angle of second triangle.

Step: 3

So, the pair of triangles in Figure 3 are congruent by the SAS congruence condition.

Correct Answer is : Figure 3

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