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Triangles Maths - Triangles

Gujarat Board (GSEB) - STD 9 - Maths (GSEB - English Medium). 55 questions in this chapter.

Question types

Triangles question types

55 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

55
Questions
6
Question groups
5
Question types
Sample Questions

Triangles questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 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.
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Q 2M.C.Q1 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
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Q 3M.C.Q1 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
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Q 4M.C.Q1 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
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Q 5M.C.Q1 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
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Q 81 Marks Question1 Mark
In $\triangle\text{ABC}$ and $\triangle\text{PQR},\angle\text{A}=\angle\text{Q}$ and $\angle\text{B}=\angle\text{R}.$ Which side of $\triangle\text{PQR}$ should be equal to side AB of $\triangle\text{ABC},$ so that the two triangles are congruent? Give reason for your answer.
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Q 112 Marks Questions2 Marks
‘If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.’ Is the statement true? Why?
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Q 122 Marks Questions2 Marks
‘If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent’. Is the statement true? Why?
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Q 132 Marks Questions2 Marks
In $\triangle\text{PQR},\angle\text{P}=70^{\circ}$ and $\angle\text{R}=30^{\circ}.$ Which side of this triangle is the longest? Give reason for your answer.
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Q 143 Marks Question3 Marks
In $\text{BA}\perp\text{AC},\text{DE}\perp\text{DF}$ such that BA = DE and BF = EC. Show that $\triangle\text{ABC}\cong\triangle\text{DEF.}$
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Q 173 Marks Question3 Marks
ABC is an isosceles triangle with AB = AC and D is a point on BC such that $\text{AD}\perp\text{BC}$ (see figure). To prove that $\angle\text{BAD} = \angle\text{CAD},$ a student proceeded as follows:In $\triangle\text{ABD}$ and $\triangle\text{ACD},$
$\text{AB}=\text{AC}$
$\angle\text{B}=\angle\text{C}$
$\angle\text{ADM}=\angle\text{ADC}$
$\therefore\triangle\text{ABD}\cong\triangle\text{ADC}$
$\angle\text{BAD}=\angle\text{CAD}$
What is the defect in the above arguments?
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Q 183 Marks Question3 Marks
In given $\text{l}\ ||\ \text{m}$ and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.
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Q 194 Marks Questions4 Marks
Question 15: Two lines l and m intersect at the point 0 and P is a point on a line n passing through the point 0 such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.
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Q 204 Marks Questions4 Marks
In D and E are points on side BC of a $\triangle\text{ABC}$ such that BD = CE and AD = AE. Show that $\triangle\text{ABC}\cong\triangle\text{ACE}.$
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Q 245 Marks Questions5 Marks
Bisectors of the angles B and C of an isosceles $\triangle\text{ABC}$ with AB = AC intersect each other at O. Show that external angle adjacent to $ \angle\text{ABC} $ is equal to $\angle\text{BOC.}$
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Q 255 Marks Questions5 Marks
M is a point on side BC of a triangle ABC such that AM is the bisector of $\angle\text{BCA}.$ Is it true to say that perimeter of the triangle is greater than 2AM? Give reason for your answer?
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