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Question

# Question 135 In each of the given pairs of triangles in given figures, using only RHS congruence criterion, determine which pairs of triangles are congruent. In case of congruence, write the result in symbolic form.

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Solution

## a) In ΔABD and ΔACD, AB = AC [given] AD = AD [common side] ∠ADB=∠ADC=90∘ By RHS congruence criterion, ΔABD≅ΔACD b) In ΔXYZ and ΔUZY, ∠XYZ=∠UZY=90∘ XZ = YU [given] ZY = ZY [common side] By RHS congruence criterion, ΔXYZ≅ΔUZY c) In ΔAEC and ΔBED, CE = DE [given] AE = BE [given] ∠ACE=∠BDE=90∘ By RHS congruence criterion, ΔAEC≅ΔBED d) Here, CD = BD - BC = 14 - 8 = 6 cm In right angled ΔABC, AC=√AB2+BC2=√62+82=√36+64 [By Pythagoras theorem] =√100=10 cm In right angled ΔCDE, DE=√CE2−CD2=√102−62=√100−36=√64=8 cm In ΔABC and ΔCDE,AC=CE=10cm BC = DE = 8 cm ∠ABC=∠CDE=90∘ By RHS congruence criterion, ΔABC≅ΔCDE e) Not possible, because there is not any right angle. f) In ΔLOM and ΔLON, LM = LN = 8 cm LO = LO [common side] ∠LOM=∠LON=90∘ By RHS congruence criterion, ΔLOM≅ΔLON

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