Geometry Problem

Click the figure below to see the complete problem 553.

Zoom

Level: High School, SAT Prep, College geometry

## Thursday, December 23, 2010

### Problem 553: Quadrilateral, Angles, Sum

Labels:
angle,
quadrilateral

Subscribe to:
Post Comments (Atom)

extend BC to E, E on AD

ReplyDeleteb = a + CED

c = d + CED

=> b + d = a + c

Join AC.

ReplyDeleteLet measure angle CAD=x and measure angle DCA=y

Hence ,measure angle BAC=a-x and measure angle BCA=c-y

In triangle ABC,by exterior angle theorem,

b=(a-x)+(c-y)...(1)

and in triangle ACD,

d=x+y...(2)

Hence, b+d=[(a-x)+(c-y)]+[x+y]

b+d=a-x+c-y+x+y

b+d=a+c.

Thus proved.