Question

Medians QT AND RS OF TRIANGLE PQR INTERSECT AT X SHOW THAT AR TRIANGLE XQR = AREA QUAD SXTP ANSWER WITH FIGURE​

Answer 1

Use MidPoint Theorem

Step-by-step explanation:

Given,

ar(ΔQTR)= AR(ΔQPT)

to p = ar(ΔXQR)= AR(ΔSXTP)

PF = In Δ PQR  as  

•         S is the mid pt of QP
•         T is the mid pt of PR

           so ST ll  QR (by midpoint theorem)

So, ar(ΔSQR)= ar(ΔTQR) (as they both stand on same base QR and between same parallels ST and QR)

subtract ar(ΔXQR) from both sides  

ar(ΔSQR)-ar(ΔXQR) = ar(ΔTQR)-ar(ΔXQR)

this implies that ar(ΔSXQ)= ar(ΔTXR)

as we know that t is the median so ar(ΔQTR) = ar(ΔQPT)

subtract ar(ΔSXQ) from ar(ΔQPT) and ar(ΔTXR) from ar(ΔQTR)

if equals are subtracted from equals then their remainders are equals (axiom 2)

this implies that ar(ΔXQR)= ar(SXTP) (by subtracting ar(ΔQTR) and ar(ΔSXQ) respectively)