In Figure 3.60, PQRS is a rhombus and its diagonals intersect each other at O.
a. Is OQ = OS? Why?
b. Is QR = SR? Why?
c. Is triangle QOR congruent to triangle SOR? By which congruence condition?
d. Is triangle QRO = triangle SRO? Why?
e. Is triangle QPO congruent to triangle SPO? By which congruence condition?
f. Is angle QPO = angle SPO? Why?
Please help
a. Is OQ = OS? Why?
b. Is QR = SR? Why?
c. Is triangle QOR congruent to triangle SOR? By which congruence condition?
d. Is triangle QRO = triangle SRO? Why?
e. Is triangle QPO congruent to triangle SPO? By which congruence condition?
f. Is angle QPO = angle SPO? Why?
Please help
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Step-by-step explanation:
Sure, here are the answers to your questions:
a. Yes, OQ = OS because the diagonals of a rhombus bisect each other.
b. Yes, QR = SR because all sides of a rhombus are equal in length.
c. Yes, triangle QOR is congruent to triangle SOR by the Side-Angle-Side (SAS) congruence condition.
d. Yes, triangle QRO is congruent to triangle SRO because they are alternate interior angles formed by transversal OR and parallel lines PQ and SR.
e. Yes, triangle QPO is congruent to triangle SPO by the Angle-Side-Angle (ASA) congruence condition.
f. Yes, angle QPO = angle SPO because they are corresponding angles formed by transversal PO and parallel lines PQ and SR.
I hope this helps! Let me know if you have any more questions.