11. ii) RP is In a quadrilateral PQRS, RP bisects LR and RQ = RS. Prove that i) PQ = PS the perpendicular bisector of QS. R R Q S S. Р P P 12. In the figure L BCD =L ADC and L ACB= LBDA. Prove that AD=BC and LA=LB.
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question 18, Laura found that the box is a little big to keep inside the locker. She realised the fact that a cubical box will exactly fit inside the locker. Find the smallest number by which 9000 must be divided so that the dimensions of the box form a perfect cube.
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Answer:
Given:
PQRS is a quadrilateral, diagonal PR bisects angle P and angle R.
To prove:
PQ = PS and RS = RQ.
Step-by-step explanation:
In ️triangle PQR & triangle ️PSR;
(A) angle QPR= angle RPR(since diagonal PR bisects angle P)
(S) Side PR=PR(common side)
(A) angle QRP= angle SRP(since diagonal PR bisects angle R)
therefore, triangle ️PQR is congruent to️ triangle PSR by ASA congruence rule.
=》side PQ= PS and RS = RQ.( by C.P.C.T.)
Hence proved.
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