Read the Source/ Text given below and answer these questions: Soh… - Vidyadip

Question

Read the Source/ Text given below and answer these questions:

Sohan wants to show gratitude towards his teacher by giving her a card made by him. He has three pieces of trapezium pasted one above the other as shown in fig. These pieces are arranged in a way that $AB \| HC \| GD \| FE.$ Also $BC = CD = DE$ and $AH = HG = GF = 6\ cm.$ He wants to decorate the card by putting up a colored tape on the nonparallel sides of the trapezium.

$i.$ Find the total length of colored tape required if $DE = 4\ cm.$
$a. 20\ cm$
$b. 30\ cm$
$c. 40\ cm$
$d. 50\ cm$
$ii. \text{ABHC}$ is a trapezium in which $AB \| HC$ and $\angle\text{A}=\angle\text{B}=45^\circ.$ Find angles $C$ and $H$ of the trapezium.
$a. 135, 130$
$b. 130, 135$
$c. 135, 135$
$d. 130, 130$
$iii.$ What is the difference between trapezium and parallelogram$?$
$a.$ Trapezium has $2$ sides, and parallelogram has $4$ sides.
$b.$ Trapezium has $4$ sides, and parallelogram has $2$ sides.
$c.$ Trapezium has $1$ pair of parallel sides, and parallelogram has $2$ pairs of parallel sides.
$d.$ Trapezium has $2$ pairs of parallel sides, and parallelogram has $1$ pair of parallel sides.
$iv.$ Diagonals in isosceles trapezoid are $ ...........$
$a.$ parallel.
$b.$ opposite.
$c.$ vertical.
$d.$ equal.
$v. \text{ABCD}$ is a trapezium where $AB \| DC, BD$ is the diagonal and $E$ is the midpoint of $AD. A$ line is drawn through $E$ parallel to $AB$ intersecting $BC$ at $F.$ Which of these is true$?$

$a. BF = FC$
$b. EA = FB$
$c. CF = DE$
$d.$ None of these

✓

Answer

$(i)$	$(b)$	$30\ cm$
$(ii)$	$(c)$	$135, 135$
$(iii)$	$(c)$	Trapezium has $1$ pair of parallel sides, and parallelogram has $2$ pairs of parallel sides.
$(iv)$	$(d)$	equal.
$(v)$	$(a)$	$BF = FC$

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