Question

plesssssss answer the 18 th and 19 th questions please!!!

Answer 1

Answer:

18th...

GIVEN...PQRS is parallelogram and X is the mid point

To prove...PS = PZ and RY = RZ

PROOF.....

Since..

∆SPX is similar to ∆SRZ (AAA)

So...

SP / PZ = SX / XR

SP / PZ = 1. (SX = XR)

SP = PZ ......... (proved)

Since...

∆YZP is similar to ∆RSZ (AAA)

YZ / YR = PZ / PS

YZ/YR = 1. (PZ = PS)

YZ = YR ......... (proved)

19th...

In ∆ADC and ∆ABE .... ∆ADE is common

Hence...

ar(∆ABE) - ar(ADE) = ar(ADC) - ar(ABE)

ar(∆BDE) = ar(∆DEC)

Since, ∆BDE and ∆DEC lie on the same base and there areas are equal hence the must be lying between same parallels...(theorem)

Therefore ... DE is parallel BC

Hence proved ....