Question

what are the conditions necessary for a triangle to be congruent. To show that the sum of angles in a quadrilateral is 360 degree​

Answer 1

Step-by-step explanation:

the 2triangles should have same side and angle

first prove the angle sum property of then add the two triangles

That will be the 360

hope will help you

Answer 2

The sum of all the angles of a quadrilateral is 360°

Step-by-step explanation:

The conditions necessary for a triangle to be congruent:

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Let ABCD be a quadrilateral and join AC

clearly,

$\angle 1 +\angle 2 = \angle A$..(1)

$\angle 3+\angle 4 = \angle B$..(2)

We know that the sum of the angles of the traingle is 180°

therefore In traingle ABC

$\angle 2+\angle 4 +\angle B = 180$°

Similarly in traingle ACD

$\angle 1 +\angle 3 +\angle D= 180$

by adding we get

$\angle 2 +\angle 4 + \angle B +\angle 1 +\angle 3 + \angle D = 180 +180$

$\angle 2 +\angle 4 + \angle B +\angle 1 +\angle 3 + \angle D =360$°

$(\angle 1 +\angle 2) +\angle B + (\angle 3+\angle4)+\angle D= 360$

using eq(1) and (2)

$\angle A +\angle B +\angle C + \angle D = 360$°

hence,

The sum of all the angles of a quadrilateral is 360°

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