TEST
Question 1
Sol:
In the given $\triangle A B C$
AD=DB and BE=EC
So D and E are mid point of AB and BC respectively
So $D E \| A C$ and $D E=\frac{1}{2} A C$
(a) DE is mid segment of $\triangle A B C$
(b) DE is parallel to AC
(C) AD=BD
(d) DE is half of AC
(e) Twice of $E C=B C$
Question 2
Sol: In the given figure,
If $Y L=L X, Y M=M Z$ and $X N=N Z$
So L,M and N are the mid points of side XY, YZ
and XZ respectively
So $L M=\frac{1}{2} \times 2, M N=\frac{1}{2} x y$
XY =10cm LM =6cm, $\angle m N Z$=$25^{\circ}$
(a) $\mathrm{Nm}=\frac{1}{2} \times y=\frac{1}{2} \times 10 \mathrm{~cm}=5 \mathrm{~cm}$
(b)$x z=2 \times L m=2 \times 6=12 \mathrm{~cm}$
(c) $\quad N Z=\frac{1}{2} \times \times 2=\frac{1}{2} \times 12=6 \mathrm{~cm}$
(d) $\angle L M N=25^{\circ}$
(If LM||XZ an MN is a transversal)
(e) $\angle Y \times z=\angle m N z=25^{\circ}$
(f)$\angle X L M=\angle X N M$ (opposite angle of a ||gm)
$=180^{\circ}-25^{\circ}=155^{\circ}$
Question 3
(IMAGE TO BE ADDED)
SOL: In $\triangle A B C$
$\mathrm{Lm} \| \mathrm{AC}$ AND $\angle m=\frac{1}{2} A C$
$\Rightarrow 32=\frac{1}{2} \times 4 n \Rightarrow 2 n=32$
$\Rightarrow n=\frac{32}{2}=16 \mathrm{~cm}$
So $n=16 \mathrm{~cm}$
Question 4
(IMAGE TO BE ADDED)
Sol: AE =EC and BD =DC
So $D E \| A B$ and $D E=\frac{1}{2} A B$
$\Rightarrow 6 n=4 n+12$
$\Rightarrow 6 n-4 n=+12$
$\Rightarrow 2 n=12$
$n=\frac{12}{2}=6$
Question 5
Sol: In the given figure
CG,EH and FJ are mid segment of $\triangle A B D, \triangle G C D$ and $\triangle G H E$ Respectively
$A B=33 \mathrm{~cm}, \angle A B C=57^{\circ}$
(a)
$\begin{aligned}&C G=\frac{1}{2} A B \\&=\frac{1}{2} \times 33=16.5 \mathrm{~cm}\end{aligned}$
(b)
$\begin{aligned} E H &=\frac{1}{2} D C \\ &=\frac{1}{2} \times \frac{1}{2} D B \\ &=\frac{1}{4} D B=\frac{1}{4} \times 44=11 \mathrm{~cm} \end{aligned}$
(C)
$\begin{aligned} F J &=\frac{1}{2} G H=\frac{1}{2} \times \frac{1}{2} G C \\ &=\frac{1}{4} G C=\frac{1}{4} \times 16.5 \mathrm{~cm}=4.125 \mathrm{~cm} \end{aligned}$
(d) $\quad M \angle D C G=\angle D B A$
=$57^{\circ}$
(e) $\begin{aligned} M \angle G H E &=\angle G C D \\ &=37^{\circ} \end{aligned}$
(f)
$\begin{aligned} M \angle F J H &=180^{\circ}-\angle G H E \\ &=180^{\circ}-57^{\circ}=123^{\circ} \end{aligned}$
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