Exercise 11B
Question 1
State whether or not the following pairs of triangles are congruent. If they are, give reasons
(a) Yes, SSS
(b) No
(c) Yes, SAS
(d) No
(e) Yes, AAS
(f) Yes, RHS
Question 2
Show by comparing angles and sides, which of the triangle given here are congruent to each other
(a) ΔABC≅ΔDEF
(b) ΔSBD≅ΔRPT , ΔCOG≅ΔLMK
(c) All triangles are congruent
(d) ΔCDE≅ΔQSB
Question 3
In the following figure, state the condition you would use to show that ΔABC and ΔCDE are congruent
Two sides and the included angle correspondingly equal (SAS)
Question 4
In the figure given alogside, ABCD is a rhombus are ΔADC and ΔABC congruent? What can you say about ΔABD and ΔBCD?
ΔADC and ΔABC are congruent
ΔABD and ΔBCD are congruent
Question 5
In this figure , TS||PQ and TS=PQ. Prove that the triangles PQR and STQ are congruent
Sol :
TS||PQ
∠STR=∠RQP [Alt. ∠s]
∠TSR=∠RSQ
TS=PQ
Two angles and the included side correspondingly equal (ASA)
∴ΔPQR and ΔSTR are congruent
Question 6
ΔPQR≅ΔLMN, If PQ=6 cm, PR=5 cm and ∠P=5 cm and ∠P=50°, find NL and ∠L if LM=5 cm and QR=MN.
NL=6 cm [∵Two sides and the included angle correspondingly equal]
∠L=50°
Question 7
In the diagrams of the following figure, name the triangle which is congruent to ΔABC, keeping the letters in the right order. State the congruence condition also
(a) AC=CX
BC=CY
∠ACB=∠XCY [Vertically opposite ∠s]
ΔACB≅ΔXCY [∵SAS rule]
(b) ∠BAC=∠QBS
∠ABC=∠BQS
AB=BQ
ΔABC≅ΔQBS [∵ASA rule]
(c) AB=AD
∠ACB=∠ACD
following RHS rule, ΔAAB≅ΔACD
(d) CA=BT
CB=AT
AB common arm
following SSS rule, ΔCBC≅ΔABT
(e) AB=AP
∠BAC=∠CAP
AC common arm
ΔABC≅ΔACP [∵SAS rule]
(f) BC=CR
∠B=∠R
AC common arm
ΔABC≅ΔACR [∵RHS rule]
Question 8
In each of the following , name the congruent triangles and state the congruence condition
(a) ΔABC≅ΔEDF [SSS rule]
(b) ΔBAC≅ΔEDF [ASA rule]
(c) ΔADB≅ΔBEA [SAS rule]
(d) ΔADB≅ΔCBD [SAS rule]
(e) ΔAED≅ΔBFC [ASA rule]
(f) ΔADE≅ΔBED [SAS rule]
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