M.C.Q

MCQ 11 Mark

In the following, write the correct answer. In $\triangle\text{PQR}$ if $\angle\text{R}=\angle\text{P}$ and $QR = 4\ cm$ and $PR = 5\ cm$. Then, the length of PQ is:

✓
$4\ cm$
B
$5\ cm$
C
$2\ cm$
D
$2.5\ cm$

Answer

Correct option: A.

$4\ cm$

In $\triangle\text{PQR}$ if $\angle\text{R}=\angle\text{P}$
NOw, $QR = 4\ cm$, Therefore, $PQ = 4\ cm$.

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MCQ 21 Mark

In the following, write the correct answer. In $\triangle\text{ABC}$ and $\triangle\text{PQR},$ if $AB = AC$, $\angle\text{C}=\angle\text{P}$ and $\angle\text{B}=\angle\text{Q}$ then the two triangles are:

✓
Isosceles but not congruent.
B
Isosceles and congruent.
C
Congruent abut not isosceles.
D
Neither congruent nor isosceles.

Answer

Correct option: A.

Isosceles but not congruent.

In $\triangle\text{ABC},$
$AB = AC$
$\angle\text{C}=\angle\text{B}$
So, is an isosceles triangle.
But it is given that,
$\angle\text{B}=\angle\text{Q}$
$\angle\text{C}=\angle\text{P}$
$\angle\text{P}=\angle\text{Q}$
So, is also an isosceles triangle.Therefore both triangle are isosceles but not congruent.

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MCQ 31 Mark

In the following, write the correct answer. Which of the following is not a criterion for congruence of triangles?

A
$SAS$
B
$ASA$
✓
$SSA$
D
$SSS$

Answer

Correct option: C.

$SSA$

We know that, two triangles are congruent, if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.
Also, criterion for congruence of triangles are $SAS$ (Side-Angle-Side), $ASA$ (Angle-Side- Angle), $SSS$ (Side-Side-Side) and $RHS$ (right angle-hypotenuse-side).
So, $SSA$ is not a criterion for congruence of triangles.

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MCQ 41 Mark

In the following, write the correct answer.
In $\triangle\text{ABC}$ and $\triangle\text{DEF},$ if $AB = AC$, $\angle\text{A}=\angle\text{D}.$ The two triangles are:

A
$BC = EF$
✓
$AC = DE$
C
$AC = EF$
D
$BC = DE$

Answer

Correct option: B.

$AC = DE$

In $\triangle\text{ABC},$
$AB = DF$
$\angle\text{A}=\angle\text{D}$
We know that, two triangles will be congruent by $ASA$ rule, if two angles and the included side of one triangle are equal to the two angles and the included side of other triangle.
$AC = DE.$

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MCQ 51 Mark

In the following, write the correct answer.Two sides of a triangle are of lengths $5\ cm$ and $1.5\ cm$. The length of the third side of the triangle cannot be:

A
$3.6\ cm$
B
$4.1\ cm$
C
$3.8\ cm$
✓
$3.4\ cm$

Answer

Correct option: D.

$3.4\ cm$

Since sum of any two sides of triangle is always greater than thrid side, so that side of the triangle cannot be $3.4\ cm$ becouse then,
$1.5\ cm + 3.4\ cm = 4.9\ cm$.

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MCQ 61 Mark

In the following, write the correct answer. If $AB = QR, BC = PR$ and $CA = PQ$, then:

A
$\triangle\text{ABC}\cong\triangle\text{QRP}$
✓
$\triangle\text{CBA}\cong\triangle\text{PRQ}$
C
$\triangle\text{BAC}\cong\triangle\text{RQP}$
D
$\triangle\text{PQR}\cong\triangle\text{BCA}$

Answer

Correct option: B.

$\triangle\text{CBA}\cong\triangle\text{PRQ}$

We know that, if is congruent to, then sides of $\triangle\text{RST}$ fall on corresponding equal sides of angles of fall on corresponding equal angles.
Here, given $AB = QR, BC = PR$ and $CA = PQ$, which shows that $AB$ covers $QR, BC$ covers $PR$ and $CA$ covers $PQ$ i.e., $A$ correspond to $Q$, $B$ correspond to $R$ and $C$ correspond to $P$.

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MCQ 71 Mark

In the following, write the correct answer.It is given that $\triangle\text{ABC}=\triangle\text{FDE}$ and $AB = 5\ cm,$ $∠\text{B} = 40°$and $∠\text{A} = 80^\circ $then which of the following is true?

A
$\text{DF}=5\text{CM}, \angle\text{F}=60^{\circ}$
✓
$\text{DF}=5\text{CM}, \angle\text{E}=60^{\circ}$
C
$\text{DE}=5\text{CM}, \angle\text{E}=60^{\circ}$
D
$\text{DE}=5\text{CM}, \angle\text{D}=40^{\circ}$

Answer

Correct option: B.

$\text{DF}=5\text{CM}, \angle\text{E}=60^{\circ}$

Given $\triangle\text{ABC}=\triangle\text{FDE}$ and AB = 5cm, $∠\text{B} = 40^\circ ,\angle\text{A}=80^{\circ}$
Since, $\triangle\text{ABC}=\triangle\text{FDE}$
$DF = AB$
$DF = 5\ cm$
$\angle\text{E}=\angle\text{C}$
$\angle\text{E}=\angle\text{C}=180^{\circ}-(\angle\text{A}+\angle\text{B})$
$\angle\text{E}=180^{\circ}-(80^{\circ}+40^{\circ})$
$\angle\text{E}=60^{\circ}$

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MCQ 81 Mark

In the following, write the correct answer. In $\triangle\text{ABC}$ if $AB = AC$ and $\angle\text{B}=50^{\circ}$ then is equal to:

A
$40^\circ$
✓
$50^\circ$
C
$80^\circ$
D
$130^\circ$

Answer

Correct option: B.

$50^\circ$

Given $\triangle\text{ABC}$ such that $AB = AC$ and $\angle\text{B}=50^{\circ}$

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MCQ 91 Mark

In the following, write the correct answer.
In $\triangle\text{ABC}$ if $BC = AB$ and $\angle\text{B}=80^{\circ}$ then is equal to:

A
$80^\circ$
B
$40^\circ$
✓
$50^\circ$
D
$100^\circ$

Answer

Correct option: C.

$50^\circ$

In $\triangle\text{ABC}$ we have
$BC = AB$
But $\angle\text{B}=80^{\circ}$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^{\circ}$
$=\angle\text{A}+80^{\circ}\angle\text{A}=180^{\circ}$
$=2\angle\text{A}=100^{\circ}$
$=\angle\text{A}=100^{\circ}\div2=50^{\circ}$

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MCQ 101 Mark

In the following, write the correct answer. In $\triangle\text{PQR},$ if $\angle\text{R}>\angle\text{Q}$ then:

A
$QR > PR$
✓
$PQ > PR$
C
$PQ < PR$
D
$QR < PR$

Answer

Correct option: B.

$PQ > PR$

Given, $\angle\text{R}>\angle\text{Q}$

$PQ > PR$.

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