Question

In trapezium PQRS , side PQ ‖ side RS , diagonals PR and QS intersect in

point O . If PQ = 20 , RS = 5 , OP= 12 then find OR. STD.10 SIMILARITY​

Answer 1

Step-by-step explanation:

1

Secondary School Math 5 points

IN A TRAPEZIUM PQRS, SIDE PQ||SIDE SR. DIAGONALS PR AND QS INTERSECT EACH OTHER AT POINT M. PQ=2RS. PROVE THAT PM=2RM AND QM=2SM.....???

Ask for details Follow Report by Sonukart4456 19.02.2019

Answers

assalterente

assalterente Ambitious

Answer:

Step-by-step explanation:

Our aim is to prove that PM = 2RM.

From the question we have that length of PQ is equal to the double length of RS, then we have:

⇒ PQ = 2RS

Now considering the triangle ΔPMQ and triangle ΔRMS, we can conclude that:

∠MPQ = ∠MRS (alternate angles)

∠MQR = ∠MSR (alternate angles)

We know can conclude that the triangle ΔPMQ are congruent with triangle ΔRMS (ΔPMQ ≅ ΔRMS), then we can conclude that:

⇒ \frac{PQ}{RS} = \frac{PM}{RM} = \frac{QM}{SM}

⇔ 2RM = PM ⇒ 2SM = QM

Hence proved.