Question

In the figure alongside , PQRS is a square. Uis the midpoint of PQ, angleRUT=90°, TU ond RQ are produced to meet at V .Prove that : TR=PT+ PQ​

Answer 1

Answer:

[tex]Given PQRS is a square and M is the midpoint of PQ

Also, RM⊥AB

In △APM & △BMQ, we have:

PM=MQ (M is the midpoint of PQ)

∠APM=∠BQM=90°

∠AMP=∠BMQ (Vertically opposite angles)

By ASA congruence axion,

△APM≅△BMQ

∴AM=MB  →1

Consider right angled △RMA

RA2=AM2+RM2 (By Pythagoras theorem)

⇒RA2=MB2+RM2→2 (From 1)

Similarly in right angled △RMB

RB2=MB2+RM2 (By Pythagoras theorem) →3

From 2 and 3 we get,

RA2=BR2

⇒AR=BR