Question

PQRS IS A PARALLELOGRAM PX AND QY ARE RESPECTIVELY THE PERPENDICULAR FROM P AND Q TO SR PRODUCED. PROVE THAT PX=QY.

Answer 1

Step-by-step explanation:

Given PQRS IS A PARALLELOGRAM PX AND QY ARE RESPECTIVELY THE PERPENDICULAR FROM P AND Q TO SR PRODUCED. PROVE THAT PX=QY

• PQRS is a parallelogram
• PX and PQ are perpendicular to SR
• QY is perpendicular to SR produced to meet QY.
• We need to prove that PX = QY (two altitudes are equal)
• Proof : Since PQRS is a parallelogram,  
•                      side PS = QR (because opposite sides of parallelogram are equal)
• Angle PSR + angle QRS = 180 degree (since sum of adjacent angles = 180 degree)
•            So PSR = 180 – QRS ------------------ 1
•      Angle YRQ + angle QRS = 180 degree (since linear pair of angles)
•               YRQ = 180 – QRS -------------------2
• From 1 and 2 we get
•               YRQ = PSR
• In triangle PXS and triangle QRY
•                                          PS = QR
•                               So PSR = YRQ
•                 Angle PXS = angle QYR (since each angle is 90 degree)
• Therefore by AAS rule
•                     Triangle PXS is congruent to triangle QRY
•                     Therefore PX = QY (Proved)

Reference link will be

https://brainly.in/question/20715586

https://brainly.in/question/2330517

Answer 2

Answer:

Step-by-step explanation:

PS IS PARALELL TO QR, SO

ANGLE PSX = ANGLE QRY

SP=QR

ANGLE PXS = QYR=90 DEGREE

SO PSX IS CONGRUENT TO QRY

BY CPCPT, PX = QY

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