IN the given figure A and B are two points on sides PQ and PR of triangle PQR such that RA is perpendicular to PQ , QB is perpendicular to PR and and AQ = BR . Prove that AR =BQ . PLEASE ANSWER FASTLY
Answers
Answer:
PB + BR = PR
PR= 10 cm
PA/PQ = 5/12.5
= 2/5
= PB/PQ = 4/10
= 2/5
as PA/PQ = PB/PQ BY Basic Proportionality Theorem they are parallel
Given : A and B are two points on sides PQ and PR of triangle PQR such that RA is perpendicular to PQ , QB is perpendicular to PR and and AQ = BR
To find : Prove that AR =BQ
Solution :
RA is perpendicular to PQ
=> ΔRAQ is right angle triangle
Apply Pythagorean theorem
AR² + AQ² = QR²
AQ = BR
=> AR² + BR² = QR²
in ΔQBR ( right angle triangle)
BQ² + BR² = QR²
Equating QR²
AR² + BR² = BQ² + BR²
=> AR² = BQ²
=> AR = BQ
QED
Hence proved
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