Geometry Problem

Click the figure below to see the complete problem 552.

Zoom

Level: High School, SAT Prep, College geometry

## Thursday, December 23, 2010

### Problem 552: Parallel lines, Transversal, Angles

Labels:
angle,
parallel,
transversal

Subscribe to:
Post Comments (Atom)

name A, B, C, D, E, F vertexes of a, b, c, d, e, f

ReplyDeleteextend AB to P, P on L2, FE to Q, Q on L1

ED to G, G on AP, BC to H, H on FQ

a + 180 - f + e + PGE = 180 - a + b + 180 - f + BHQ

2a + e + PGE = 2f + b + BHQ (1)

PGE = 180 + c - b - d

BHQ = 180 - c - e + b

substitute to (1)

2c + 2e + 2a = 2d + 2b + 2f

c + e + a = d + b + f

http://img843.imageshack.us/img843/3136/problem552.png

ReplyDeleteMake polygon with 7 sides per attached pictures

Summation all internal angles=5*180=900

90-f+e+360-d+c+360-b+a+90=900

So a+c+e=b+d+f

Peter Tran