Question

А
3. Two sides AB and BC and median AM
of one triangle ABC are respectively
equal to sides PQ and QR and median
PN of APQR (see Fig. 7.40). Show that:
(1) A ABMEAPON
(*) ABC=APQR
B.
M
Fig. 7.40​

Answer 1

Explanation:

Given: Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆PQR. (ii) ∆ABC ≅ ∆PQR. ∴ ∠ABM = ∠PQN | C.P.C.T. ∆ABC is an isosceles triangle in which AB = AC.

Answer 2

$\huge\underline\mathbb\purple{TRIANGLES}$

In $\triangle$ AMB and $\triangle$ PQN

=> AB = PQ (given)

=> AM = PM (given)

=> BC = QR

1/2 BC = 1/2 QN (as median cuts a triangle in 2 equal parts.)

$\therefore$ Triangle AMB is congurente to Triangle PQN (SSS rule)

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In $\triangle$ ABC and $\triangle$ PQR

=> AB = PQ (given)

=> BC = QR (given)

=> $\angle$ B = $\angle$ C (CPCT)

$\therefore$ Triangle ABC is congurent to traingle PQR (SAS rule)

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