#### Solved Examples and Worksheet for SSS and SAS Postulates-Triangle Congruence

Q1In triangles ABC and PQR, AB = 3.5 cm, BC = 7.4 cm, AC = 5.4 cm, PQ = 3.5. cm, QR = 7.4 cm and PR = 5.4 cm. Examine whether the two triangles are congruent or not. If yes, what is the congruence rule and congruence relation in symbolic form ? A. ΔABC ≅ ΔPQR (SSS Congruence Rule/Criterion)
B. ΔABC ≅ ΔPQR (SAS Congruence Rule/Criterion)
C. ΔABC ≅ ΔPQR (ASA Congruence Rule/Criterion)
D. ΔABC ≅ ΔPQR (RHS Congruence Rule/Criterion)

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)
Q2What additional information is needed to prove that ΔADB ≅ ΔCDB by the SAS Postulate ? A. ∠ABD = ∠CBD
C. ∠ABD = ∠CDB

Step: 1
AB¯CB¯
[Given.]
Step: 2
BD¯BD¯
[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
Q3Which of the following can be applied directly to prove that ΔABC ≅ ΔEDC ? A. SAS postulate
B. SSS postulate
C. ASA postulate
D. SAA postulate

Step: 1
AC¯CE¯
[Given.]
Step: 2
BC¯CD¯
[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
Q4Which of the following can be applied directly to prove that ΔABD ≅ ΔCBD ? A. ASA postulate
B. SAA postulate
C. SSS postulate
D. SAS postulate

Step: 1
AB¯BC¯
[Given.]
Step: 2
[Given.]
Step: 3
BD¯BD¯
[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
Q5Supply the reason to complete the proof below: A. AAS postulate
B. SSS postulate
C. ASA postulate
D. SAS 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
Q6What additional information is needed to prove that ΔQRP ≅ ΔTRS by the SAS Postulate ? A. QR¯ST¯
B. QR¯TR¯
C. ∠PQR = ∠RTS
D. PQ¯RS¯

Step: 1
PR¯SR¯
[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.
Q7Supply the reason to complete the proof below: A. ASA postulate
B. SSS postulate
C. SAS postulate
D. AAS postulate

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
Q8What additional information is needed to prove that ΔPQS ≅ΔRSQ by the SSS Postulate ? A. PS¯QS¯
B. PQ¯QR¯
C. ∠PQS = ∠RSQ
D. PS¯QR¯

Step: 1
PQ¯RS¯
[Given.]
Step: 2
QS¯QS¯
[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.
Q9What additional information is needed to prove that ΔABC ≅ ΔZYX by the SAS Postulate ? A. AB¯XZ¯
B. ∠CAB = ∠XZY
C. AB¯ZY¯
D. AC¯XZ¯

Step: 1
BC¯YX¯
[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.
Q10Which of the following pair of triangles are congruent by the SAS congruence condition? A. Figure 1
B. Figure 4
C. Figure 3
D. Figure 2

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