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:-**

Base^{2} + Height^{2} = Hypotenuse^{2}

In Δ ABC

AC^{2} = 6^{2} + 8^{2}

AC^{2} = 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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If are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

NCERT Mathematics

In Fig. 6.57, state the three pairs of equal parts in ∆ABC and ∆EOD. Is ∆ABC ≅ ∆EOD? Why?

NCERT - Exemplar Mathematics

In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT.

(i) Is ∆QSR ≅ ∆RTQ? Give reasons.

(ii) Is ∠PQR = ∠PRQ? Give reasons.

NCERT - Exemplar MathematicsIn 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:

NCERT - Exemplar Mathematics

Explain, why

NCERT Mathematics