How to Check if the Given Triangles are Congruent with Given Triangles :
Here we are going to see some example problems to check if the given triangles are congruent with given triangles.
Question 1 :
Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:
In triangle ABC, and triangle PQR
AB = QP
BC = RQ
From the given information, the triangles are not congruent. If AC and RP were equal, then both the triangles will be congruent by using SSS criterion.
In triangle ABD, in triangle BDC
AB = DC (S)
AD = BC (S)
DB = DB (S)
Hence the triangle ABD and BDC are congruent using the criterion SSS.
In triangle TXP and PXZ
YX = ZX (S)
YP = PZ (S)
PX = PX (S)
Hence the triangles TXP and PXZ are congruent using the criterion SSS.
In triangle ABO and ODC
AO = OC (S)
<ABO = <ODC (A)
<AOB = <DOC (A)
By using the criterion ASA triangle ABO and ODC are congruent.
In triangle AOB, triangle ODC
BO = DO (S)
AO = OC (S)
<AOB = <ODC (A)
By using the criterion SAS the triangles are AOB and ODC.
In triangle ABM and AMC
AB = AC (S)
<AMB = <AMC (A)
AM = AM (S)
Hence the triangles ABM and AMC are congruent.
Question 2 :
ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°; ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent
AB = EF (S)
<ABC = <EDF (A)
<BCA = <DEF (A)
Hence the triangles are congruent.
Question 4 :
Find all the three angles of the ΔABC
<ACB = <ABC + <BAC
4x - 15 = 2x - 5 + x + 35
4x - 2x - x = 35 - 5 + 15
x = 45
4x - 15 = 4(45) - 15 = 165
2x - 5 = 2(45) - 5 = 85
x + 35 = 45 + 35 = 80
Hence the required angles are 165, 85 and 80.
After having gone through the stuff given above, we hope that the students would have understood, "How to Check if the Given Triangles are Congruent with Given Triangles"
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