SOLUTION: Write a two-column proof that the sum of the angle measures pf a quadrilateral is 360 degrees. Begin by drawing quadrilateral ABCD. (hint: you will have to draw one auxiliary line.

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Question 526318: Write a two-column proof that the sum of the angle measures pf a quadrilateral is 360 degrees. Begin by drawing quadrilateral ABCD. (hint: you will have to draw one auxiliary line.)
Answer by solver91311(24713) (Show Source):
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Draw a diagonal in the quadrilateral forming two triangles.

Label the angles in one triangle , , and . Label the angles in the other triangle , , and . Arrange the labels so that and are adjacent and and are adjacent. Then label the angle that is the combination of and with a and the angle that is the combination of and with a . The four interior angles of the quadrilateral should then be , , , and and we want to prove that

The interior angles of a triangle sum to 180 degrees (you find the theorem that says so; it is in your Geometry book somewhere.)

So

and

so

But

by the Angle Sum Postulate and

by the Angle Sum Postulate

Then

By Addition Associativity

And then

By Substitution of Equality. Q.E.D.

John

My calculator said it, I believe it, that settles it