1. Prove Theorem 3.2.1: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Specifically, given quadrilateral PQRS below with diagonals PR and SQ bisecting each other at point T, prove that quadrilateral PQRS is a parallelogram. Hint: Prove that AQTR E ASTP, and from that conclude that 26 25 and therefore QR || PS. Similarly, proving that AQTP S ASTR will lead to the conclusion that QP || RS.] 6. 8. 3. 4. 2 T
1. Prove Theorem 3.2.1: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Specifically, given quadrilateral PQRS below with diagonals PR and SQ bisecting each other at point T, prove that quadrilateral PQRS is a parallelogram. Hint: Prove that AQTR E ASTP, and from that conclude that 26 25 and therefore QR || PS. Similarly, proving that AQTP S ASTR will lead to the conclusion that QP || RS.] 6. 8. 3. 4. 2 T
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3.2. PARALLELOGRAMS
95
Intermediate Exercises
1. Prove Theorem 3.2.1: If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a parallelogram. Specifically, given
quadrilateral PQRS below with diagonals PR and SQ bisecting each
other at point T, prove that quadrilateral PQRS is a parallelogram.
Hint: Prove that AQTR ASTP, and from that conclude that 26 2
25 and therefore QR || PS. Similarly, proving that AQTP S ASTR
will lead to the conclusion that QP || RS.]
R.
6
8.
4.
2T
PI](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff01920e7-b500-4774-ab30-ea02b760777b%2F8ac20dd6-2717-48b6-8dfc-139f6b8cfd71%2Fj2dcpyg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.2. PARALLELOGRAMS
95
Intermediate Exercises
1. Prove Theorem 3.2.1: If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a parallelogram. Specifically, given
quadrilateral PQRS below with diagonals PR and SQ bisecting each
other at point T, prove that quadrilateral PQRS is a parallelogram.
Hint: Prove that AQTR ASTP, and from that conclude that 26 2
25 and therefore QR || PS. Similarly, proving that AQTP S ASTR
will lead to the conclusion that QP || RS.]
R.
6
8.
4.
2T
PI
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