Sarthaks Test
+1 vote
1.4k views
in Mathematics by (35.6k points)

P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove that CQ is parallel to AP. Prove also that AC bisects PQ.

1 Answer

+1 vote
by (61.7k points)
selected by
 
Best answer

We know that, diagonals of a parallelogram bisect each other

OA = OC and OB = OD 

Since P and Q are point of intersection of BD 

BP = PQ = QD 

Now, OB = OD and BP = QD 

OB - BP = OD - QD 

OP = OQ 

Thus in quadrilateral APCQ, we have 

OA = OC and OP = OQ 

diagonals of quadrilateral APCQ bisect each other 

APCQ is a parallelogram 

Hence AP || CQ

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...