SOLUTION: PQRS is a quadrilateral of which the diagonals PR and QS intersect at X so that PX=XQ and the sides PQ,SR are parallel. Prove that XS=XR

Algebra ->  Triangles -> SOLUTION: PQRS is a quadrilateral of which the diagonals PR and QS intersect at X so that PX=XQ and the sides PQ,SR are parallel. Prove that XS=XR      Log On


   

Question 1036700: PQRS is a quadrilateral of which the diagonals PR and QS intersect at X so that PX=XQ and the sides PQ,SR are parallel. Prove that XS=XR
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!



1. ΔPXQ is isosceles           1. PX = XQ        
2. ∠XPQ = ∠XQP                2. base angles of isosceles ΔPXQ
3. ∠XPQ = ∠XRS                3. alternate interior angles when
                                  ∥ lines PQ,SR are cut by 
                                  transversal PR.
4. ∠XQP = ∠XSR                4. alternate interior angles when
                                  ∥ lines PQ,SR are cut by 
                                  transversal QS.
5. ∠XSR=∠XQP=∠XPQ=∠XRS        5. Things = to = things are = to 
                                   each other, from steps 4,2,3

6. ΔSXR is isosceles           6. Base angles equal
7. XS = XR                     7. Legs of isosceles ΔSXR are equal. 

Edwin