Question

PQRS is a rhombus.Diagonals PR and QS intersect at o.Prove that all the four triangles so formed are congruent.

Answer 1

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Answer 2

all four triangles are congruent

Step-by-step explanation:

given : PQRS is a rhombus.Diagonals PR and QS intersect at o

to prove : all the four triangles so formed are congruent

proof :

in triangle POQ  and SOR

$\angle POQ = \angle SOR$ (vertical opposite angle )

OP = OR (Diagonals PR and QS intersect at o.)

PQ = SR (sides of rhombus )

then by SAS congurency rule

$\bigtriangleup POQ \cong \bigtriangleup SOR$

in triangle POS and POQ

OP = OP (COMMON)

OS = OQ

PS = PQ (sides of rhombus)

therefore

$\bigtriangleup POS \cong \bigtriangleup POQ$..1

similarly

$\bigtriangleup POS \cong \bigtriangleup QOR$ ...2, $\bigtriangleup POQ \cong \bigtriangleup POR$...3

from eq 1, 2 and 3

all four triangles are congruent

hence , proved

#Learn more:

In the given figure , PQRS is a parallelogram . Diagonal PR and QS intersect at O

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