Question

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.

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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(a) AD=DE; and
(b) ∠DAE=1/2(∠C−∠B)
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