Question

In the figure, two sides AB and BC and the median AD of A ABC are respectively equal to
the two sides PQ and QR and the median PM of the other A PQR. Prove that
(i)triangle ABD is congruents to triangle PQM
(ii)triangle ABC is congruents to triangle ​

Answer 1

Answer:

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Answer 2

Given:

Two sides AB,BC and the median AD of ∆ ABC are respectively equal to two sides PQ,QR and median PS of ∆PQR.

To prove:

(i) ∆ADB≈ ∆PSQ

(ii) ∆DC≈∆PSR

Proof:

i) In ∆ADB and ∆PSQ

AB=PQ

AD=PS

BD=QS

[BC=QR=>BC/2 =QR/2

=>BD=QS and DC=SR]

Therefore,

∆ADB≈∆PSQ

[SSS congruence rule]

ii)In ∆ADC and ∆PSR

AD=PS (side)

<ADC=<PSR [Angle]

DC =SR (side)

Therefore,

∆ADC≈∆PSR

[SAS congruence rule]