Question

Two sides AB and BC and median AM of one
triangle ABC are respectively equal to sides xy and yz and
mediun xT of triqngle xyz. Show that
a) triangle = triangle xyT
b) triangle ABC = triangle xyz​

Answer 1

Answer:

I can't remember the answer sorry

Answer 2

Answer:

☞Congruence of triangles:

Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.

In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.

It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

☞Criteria for congruence of triangles:

There are 4 criteria for congruence of triangles.

☞SAS( side angle side):

Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.

☞SSS(side side side):

Three sides of One triangle are equal to the three sides of another triangle then the two Triangles are congruent.

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We know that median bisects opposite side. Use this property and then show that given parts by using SSS and SAS congruence rule.

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☞Solution:

☞Given:

AM is the median of ∆ABC & PN is the median of ∆PQR.

AB = PQ, BC = QR & AM = PN

☞To Show:

(i) ΔABM ≅ ΔPQN

(ii) ΔABC ≅ ΔPQR

☞Proof:

Since AM & PN is the median of ∆ABC

☞(i) 1/2 BC = BM &

1/2QR = QN

(AM and PN are median)

Now,

BC = QR. (given)

⇒ 1/2 BC = 1/2QR

(Divide both sides by 2)

⇒ BM = QN

In ΔABM and ΔPQN,

AM = PN (Given)

AB = PQ (Given)

BM = QN (Proved above)

Therefore,

ΔABM ≅ ΔPQN

(by SSS congruence rule)

∠B = ∠Q (CPCT)

☞(ii) In ΔABC & ΔPQR,

AB = PQ (Given)

∠B = ∠Q(proved above in part i)

BC = QR (Given)

Therefore,

ΔABC ≅ ΔPQR

( by SAS congruence rule)

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