Sarthaks Test
0 votes
in Mathematics by (35.6k points)

ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the mid-points of the sides, in order, is a rectangle.

1 Answer

0 votes
by (61.7k points)
selected by
Best answer

Given: A kite ABCD having AB = AD and BC = CD P, Q, R, S are the midpoint of sides AB, BC, CD, and DA respectively PQ, QR, RS and spare joined 

To prove: PQRS is a rectangle


Thus, in quadrilateral PQRS, a pair of opposite sides are equal and parallel. So PQRS is a parallelogram. Now, we shall prove that one angle of parallelogram PQRS it is a right angle 

Since AB = AD

Now, transversal PS cuts parallel lines SR and PQ at S and P respectively.

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.