SOLUTION: Let {{{highlight(cross(Angle))}}} XOY be an angle and PZ be an interval. Construct an arc with centre O meeting OX at A and OY at B. With the same radius, construct an arc with cen

Algebra ->  Finance -> SOLUTION: Let {{{highlight(cross(Angle))}}} XOY be an angle and PZ be an interval. Construct an arc with centre O meeting OX at A and OY at B. With the same radius, construct an arc with cen      Log On


   

Question 1195538: Let highlight%28cross%28Angle%29%29 XOY be an angle and PZ be an interval. Construct an arc with centre O meeting OX at A and OY at B. With the same radius, construct an arc with centre P, meeting PZ at F. With radius AB and centre F, construct an arc meeting the second arc at G.
(a) Prove that triangle AOB is congruent to triangle GPF.
(b) Hence, prove that Angle AOB = Angle FPG.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
(a)  Triangle AOB is congruent to triangle GPF due to SSS-test of congruency for triangles,

     since they have congruent (equal) sides by construction.



(b)  Angle AOB = Angle FPG  as the corresponding angles in congruent triangles AOB and GPF.

Solved, answered and explained.