Question

In the given figure, A and B are two points on sides

PQ and PR of ∆PQR such that RA ⊥ PQ, QB ⊥ PR

and AQ = BR. Prove that AR = BQ.​

Answer 1

Answer:

AR = BQ (CPCT)

Step-by-step explanation:

By DOING congruent

Let the intersecting points of line AR and BQ be O

In triangles BQR and ARQ

Angle QAR = Angle RBQ ( Given )

AQ = BR ( given )

Angle AOQ = Angle BOR ( vertically opposite angles

By ASA rule

Hence triangles AQR and BRQ are congruent to each other.

therefore, AR = BQ ( CPCT )

Hope it helps you

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Answer 2

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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