Q. 1354.0( 4 Votes )

In each of the given pairs of triangles of Fig. 6.43, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form:






Answer :

Formula Used/Theory:-


RHS congruence criterion is in which hypotenuse and one side are equal in both the triangles


(a) AC = AB (Hypotenuse)


AD = AD (common in both triangles)


Δ ADB and Δ ADC are congruent by RHS


∆ADB ∆ADC


Result:- Δ ADB and Δ ADC are congruent by RHS


(b) XZ = YU (Hypotenuse)


YZ = YZ (common in both triangles)


Δ XYZ and Δ UZY are congruent by RHS


∆XYZ ∆UZY


Result:- Δ XYZ and Δ UZY are congruent by RHS


(c) AE = EB (Hypotenuse)


CE = ED


Δ ACE and Δ BDE are congruent by RHS


∆ACE ∆BDE


Result:- Δ ACE and Δ BDE are congruent by RHS


(d) Pythagoras theorem:-


Base2 + Height2 = Hypotenuse2


In Δ ABC


AC2 = 62 + 82


AC2 = 36 + 64


AC = √100


AC = 10cm


CD = BD – BC = 14 cm – 8 cm


CD = 6cm


AC = CE (Hypotenuse)


AB = CD


Δ ABC and Δ CDE are congruent by RHS


∆ABC ∆CDE


Result:- Δ ABC and Δ CDE are congruent by RHS


(e) XY = XY (Common Hypotenuse)


XZ≠YU


XU≠YZ


Δ XYZ and Δ XYU are not congruent by RHS


Result:- Triangles are not congruent


(f) LM = LN (Hypotenuse)


LO = LO


Δ LOM and Δ LON are congruent by RHS


∆LOM ∆LON


Result:- Δ LOM and Δ LON are congruent by RHS


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