Question

If in triangle ABC and Triangle XYZ we have AB = XY, AC = XZ, but...

If in triangle ABC and Triangle XYZ we have AB = XY, AC = XZ, but m<A > m<X, then BC > YZ. Conversely, if BC > YZ then m<A > m<X.

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Answer #1

Given : and are triangles. AB = XY , AC = XZ, but

Prove that :

Proof :

In and ,

....... (given)...... 1.

........ (given)...... 2.

Suppose If IT WAS GIVEN

Then ................... (By Congruence rule: If two sides and its including angle are congruent to the corresponding two sides and including angle of another triangle, then both the sides are congruent by S-A-S test)

.................. (Corresponding sides of congruent triangles)

But GIVEN is :

......... (Theorem : Side opposite to Greater angle is Greater....)....(3)

Conversely,

If GIVEN IS :

then ........... (Converse of above (3) : Angle opposite to Greater side is Greater......)

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