Question

hey
PR BISECTS QS AT RIGHT ANGLES.PROVE THAT PQ=PS AND QR=RS
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Answer 1

As we know that diagonals bisect the angles.

Therefore,

angle PQM = angle RQM •••(i)

& angle PSM = angle RSM •••(ii)

# In triangles PQM and PSM,

/_ PMQ = /_ PMS [ Each 90°]

or, QM = QS [Given]

& /_ PQM = /_ PSM [From (i)]

.°. Both triangles are congruent by ASA congruence rule.

i.e, PQ = PS ( by cpct)

# //ly,

Triangles RQM and RSM are congruent.

.°. QR = RS ( by cpct)

#$# HOPE YOU UNDERSTAND #$#

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