Question

pls help me I need answers of these 5 Q.

Answer 1

Q.6
in a ll gm the opposite angles are equal
5x-3=4x+12
x=15
adjacent angles of a parallelogram are supplementary
angle₁+angle₂= 180
angle₂=108
Q.7
use mid point theorem i.e the line joining the mid points of 2 sides in a triangle is equal to half of the 3rd side
Q.8 in ∆ ABC BE is median
AE= EC =1/2 AC......(1)
in ∆ BEC
D is the midpoint of BC and BE||DF
F is mid point of EC [mid point theorem ]
CF=EF=1/2 EC......(2)
Using (1)&(2)
CF = 1/4 AC
Q.9 use mid point theorem of trapezium ,i.e, the line joining the mid points of the non || sides of trapezium is || to the || sides and equal to half of their sum
Q.10
In ∆ CDR
AP||CQ
AP||CR
P is the mid point of CD
A is mid of RD [ mid point theorem]
AD= AR
AD =BC [opposite sides of || gm ]
BC=AR
In ∆ ARQ & ∆ QBC
< AQR =< CQB [vertically opposite]
< RAQ= < QBC [Interior alternate]
BC = AR [ Proved above]
∆ ARQ≅∆ QBC [AAS]
QC=QR [C.P.C.T]