Question

State which pair of triangles are congruent by RHS congruence condition. If congruent write the triangle in symbolic form.​

Answer 1

$\Large{\red{\underline{\underline{\tt{AnSweR:}}}}}$

Given,

to find out wether the given figures are 

Congruent using RHS

(i)  Congruence rule

so, Now let us consider figure (i)

as per RHS congruence rule.

LQ=LF=90o (∵ given)

PR=FD (given)

PQ=DE (∵ given in figure (i))

∴ △PQR is not congruence to △DEF

(ii) Now let us consider figure (i)

as per RHS congruence rule

LC=LD=90o (∵ given )

AC=BD (∵ given)

AB=AB (∵ common side)

∴ △ABC≅△ABD

(iii) Now let us consider figure (iii)

as per RHS congruence rule we get,

∠B=∠D=90o (∵ given)

AB=AD (∵ given)

BC=CD (∵ given)

∴ △ABC≅△ADC

(iv) Let us consider figure (iv)

as per RHS congurence rule we get,

∠S=∠S=90o (common angle )

PQ=PR (∵ given)

QS=SR (∵ common base)

∴ △PSQ≅△PSR

Answer 2

AnSweR:

Given,

to find out wether the given figures are

Congruent using RHS

(i) Congruence rule

so, Now let us consider figure (i)

as per RHS congruence rule.

LQ=LF=90o (∵ given)

PR=FD (given)

PQ=DE (∵ given in figure (i))

∴ △PQR is not congruence to △DEF

(ii) Now let us consider figure (i)

as per RHS congruence rule

LC=LD=90o (∵ given )

AC=BD (∵ given)

AB=AB (∵ common side)

∴ △ABC≅△ABD

(iii) Now let us consider figure (iii)

as per RHS congruence rule we get,

∠B=∠D=90o (∵ given)

AB=AD (∵ given)

BC=CD (∵ given)

∴ △ABC≅△ADC

(iv) Let us consider figure (iv)

as per RHS congurence rule we get,

∠S=∠S=90o (common angle )

PQ=PR (∵ given)

QS=SR (∵ common base)

∴ △PSQ≅△PSR

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