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:

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