Question

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.....???

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation: