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MATHS M.C.Q

Triangles · Rajasthan Board (RBSE) STD 9 (Rajasthan - English Medium). 11 questions.

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Question 11 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:
  1. Isosceles but not congruent.
  2. Isosceles and congruent.
  3. Congruent abut not isosceles.
  4. Neither congruent nor isosceles.
Answer
  1. Isosceles but not congruent.
Solution:
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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Question 21 Mark
In the following, write the correct answer.
Which of the following is not a criterion for congruence of triangles?
  1. SAS
  2. ASA
  3. SSA
  4. SSS
Answer
  1. SSA
Solution:
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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Question 31 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:
  1. BC = EF
  2. AC = DE
  3. AC = EF
  4. BC = DE
Answer
  1. AC = DE
Solution:
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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Question 41 Mark
In the following, write the correct answer.
D is point on the side BC of a $\triangle\text{ABC}$ such that AD bisects Then.
  1. BC = CD
  2. BA > BD
  3. BD > BA
  4. CD > CA
Answer
  1. BA > BD
Solution:
In $\triangle\text{ADC},$ AB > BD.
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Question 51 Mark
In the following, write the correct answer.
In $\triangle\text{PQR}$ if $\angle\text{R}=\angle\text{P}$ and QR = 4cm and PR = 5cm. Then, the length of PQ is:
  1. 4cm
  2. 5cm
  3. 2cm
  4. 2.5cm
Answer
  1. 4cm
Solution:
In $\triangle\text{PQR}$ if $\angle\text{R}=\angle\text{P}$NOw, QR = 4cm, Therefore, PQ = 4cm.
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Question 61 Mark
In the following, write the correct answer.
If AB = QR, BC = PR and CA = PQ, then:
  1. $\triangle\text{ABC}\cong\triangle\text{QRP}$
  2. $\triangle\text{CBA}\cong\triangle\text{PRQ}$
  3. $\triangle\text{BAC}\cong\triangle\text{RQP}$
  4. $\triangle\text{PQR}\cong\triangle\text{BCA}$ 
Answer
  1. $\triangle\text{CBA}\cong\triangle\text{PRQ}$
Solution:
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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Question 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 $∠\text{A} = 80°$then which of the following is true?
  1. $\text{DF}=5\text{CM}, \angle\text{F}=60^{\circ}$
  2. $\text{DF}=5\text{CM}, \angle\text{E}=60^{\circ}$
  3. $\text{DE}=5\text{CM}, \angle\text{E}=60^{\circ}$
  4. $\text{DE}=5\text{CM}, \angle\text{D}=40^{\circ}$
Answer
  1. $\text{DF}=5\text{CM}, \angle\text{E}=60^{\circ}$
Solution:
Given $\triangle\text{ABC}=\triangle\text{FDE}$ and AB = 5cm, $∠\text{B} = 40°,\angle\text{A}=80^{\circ}$
Since, $\triangle\text{ABC}=\triangle\text{FDE}$ DF = AB
DF = 5cm
$\angle\text{E}=\angle\text{C}$
$\angle\text{E}=\angle\text{C}=180^{\circ}-(\angle\text{A}+\angle\text{B})$
$\angle\text{E}=180^{\circ}-(80^{\circ}+40^{\circ})$
$\angle\text{E}=60^{\circ}$
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Question 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:
  1. 40º
  2. 50º
  3. 80º
  4. 130º
Answer
  1. 50º
Solution:
Given $\triangle\text{ABC}$ such that AB = AC and $\angle\text{B}=50^{\circ}$
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Question 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:
  1. 80º
  2. 40º
  3. 50º
  4. 100º
Answer
  1. 50º
Solution:
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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Question 101 Mark
In the following, write the correct answer.
In $\triangle\text{PQR},$ if $\angle\text{R}>\angle\text{Q}$ then:
  1. QR > PR
  2. PQ > PR
  3. PQ < PR
  4. QR < PR
Answer
  1. PQ > PR
Solution:
Given, $\angle\text{R}>\angle\text{Q}$PQ > PR.
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Question 111 Mark
In the following, write the correct answer.Two sides of a triangle are of lengths 5cm and 1.5cm. The length of the third side of the triangle cannot be:
  1. 3.6cm
  2. 4.1cm
  3. 3.8cm
  4. 3.4cm
Answer
  1. 3.4cm
Solution:
Since sum of any two sides of triangle is always greater than thrid side, so that side of the triangle cannot be 3.4cm becouse then,
1.5cm + 3.4cm = 4.9cm.
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