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: A.
View full solution →Question types
Triangles question types
54 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
54
Questions
6
Question groups
5
Question types
01
M.C.Q
10 Q→021 Marks Question
5 Q→032 Marks Questions
3 Q→043 Marks Question
12 Q→055 Marks Questions
2 Q→064 Marks Questions
22 Q→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.
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.
- BIsosceles and congruent.
- CCongruent abut not isosceles.
- DNeither congruent nor isosceles.
Answer: A.
View full solution →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: C.
View full solution →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:
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: B.
View full solution →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: D.
View full solution →Is it possible to construct a triangle with lengths of its sides as $8\ cm, 7\ cm$ and $4\ cm?$ Give reason for your answer.
View full solution →It is given thet $\triangle\text{PQR}\cong\triangle\text{EDF},$ then Is it true to say that $PR = EF?$ Given reason for your answer.
View full solution →It is given thet $\triangle\text{ABC}\cong\triangle\text{RPQ}.$ Is it true to say thet $BC = QR?$ Why$?$
View full solution →Is it possible to construct a triangle with lengths of its sides as $9\ cm, 7\ cm$ and $17\ cm?$ Give reason for your answer.
View full solution →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.
View full solution →‘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?
‘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?
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.
View full solution →In following figure if $AD$ is the bisector of $\angle\text{BAC},$ then prove that $AB > BD.$
View full solution →$ABCD$ is a quadrilateral such that diagonal $AC$ bisects the angles $A$ and $C$. Prove that $AB = AD$ and $CB = CD$.
View full solution →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?
View full solution →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?
Is it possible to construct a triangle with lengths of its sides as $4\ cm, 3\ cm$ and $7\ cm$? Give reason for your answer.
View full solution →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.
View full solution →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 $\angle\text{BOC.}$
View full solution →$M$ 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$?$
View full solution →$O$ is a point in the interior of a square $ABCD$ such that $OAB$ is an equilateral triangle. Show that $ΔOCD$ is an isosceles triangle.
View full solution →$ABC$ is an isosceles triangle with $AB = AC$ and $BD, CE$ are its two medians. Show that $BD = CE.$
View full solution →In $D$ and $E$ are points on side $BC$ of a $\triangle\text{ABC}$ such that $BD = CE$ and $AD = AE.$ Show that $\triangle\text{ABC}\cong\triangle\text{ACE}.$
View full solution →$ABCD$ is quadrilateral such that $AB = AD$ and $CB = CD.$ Prove that $AC$ is the perpendicular bisector of $BD.$
View full solution →In a triangle $ABC, D$ is the mid-point of side AC such that $\text{BD}=\frac{1}{2}\text{AC}.$Show that $\angle\text{ABC}$ is a right angle.
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