case /data -based (4 Marks)

MCQ 14 Marks

In the triangle $ABC$ below, $AC = BC.$ In the triangle $DCE, \angle CED = 90^\circ .$

$1$.What is the value of $'x\ ’?$

A
$40$
✓
$50$
C
$60$
D
$70$

Answer

Correct option: B.

$50$

$ 50$

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Question 24 Marks

In the triangle $XYZ,$ the median $XP$ is half the length of the side $YZ.$
In the triangle, $XZQ, XZ = ZQ.$

$1.$ What is the measure of $\angle ZXQ?$

Answer

$9. 30$
$30^\circ $

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Question 34 Marks

A shelf with a triangular frame is ixed on a wall as shown below.

The lengths of the rods used in the shaded triangular frame are $48\ cm, 55\ cm$ and $73\ cm.$
$1.$ What is the type of the shaded triangle$?$
$A.$ Obtuse triangle
$B.$ Isosceles triangle
$C.$ Equilateral triangle
$D. $ Right-angled triangle
$2.$ What can be the height of the shelf$?$

Answer

$7. D.$ Right-angled triangle
$8.$ Accept any of the two lengths, either $48$ or $55$
● $48\ cm$
● $55\ cm$

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Question 44 Marks

In the figure shown below, $PQR$ is a straight line.

The measure of $\angle PXQ = 20^\circ .$
$1.$ What is the measure of $\angle PXR?$

Answer

$6. 60$
$60^\circ $

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Question 54 Marks

Pratibha made a paper lag by pasting an isosceles right triangle on a stick.

$1.$ What is the measure of $\angle ACD?$

Answer

$5. 135^\circ$
$135$

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Question 64 Marks

Anshu cuts a paper triangle $ABC.$
He folds the paper perpendicular to $BC$ such that it passes through the vertex $A.$ He marks the
point where the fold crosses $BC$ as $M.$ He unfolds the paper.
He again folds all the three corners such that vertices $A, B$ and $C$ touch $M$ without overlapping.

Radhika performs a similar activity. She marks $M$ by folding $\triangle ABC$ such that it halves the side
BC. When she folds the three corners such that vertices $A, B$ and $C$ touch $M,$ unlike Anshu, the
paper corners overlap.
$1.$ What can be the reason for overlapping$?$
$2.$ Why is the existence of a triangle with an exterior angle of measure $180^\circ $ not possible$?$

Answer

$3.$ Accept answers in which differentiation between median and altitude is evident.
● Anshu marked the altitude of the side $BC,$ while Radhika marked the median of the side $BC.$
$4.$ The explanation involves the angle sum property of a triangle.
● An exterior angle is the sum of its opposite interior angles. If the sum of two angles is $180^\circ ,$ the measure of the third angle will be $0^\circ .$ Thus no triangle will be formed.

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Question 74 Marks

In an equilateral triangle $ABC,$ the length of $AC = 10\ cm$ and altitude $AD = 6\ cm.$ $P$ is a point on $AB.$

The length of $BP = 4x – 1.$ The length of $PA = 3x+ 4$
$1.$ What is the length of $BP?$
$A. 1\ cm$
$B. 3\ cm$
$C. 5\ cm$
$D. 10\ cm$
$2.$ What is the length of the median on $BC?$
$A. 3\ cm$
$B. 5\ cm$
$C. 6\ cm$
$D. 10\ cm$

Answer

$1. B. 3\ cm$
$2. C. 6\ cm$

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MATHS case /data -based (4 Marks)

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