Can you construct a $\triangle ABC$ in which $AB =5 cm, BC =4 cm$ and $AC =9 cm$ ? Give reason.
View full solution →Question types
Triangles question types
193 questions across 5 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
193
Questions
5
Question groups
5
Question types
01
[2 Mark Question Answer]
53 Q→02[3 marks sum]
57 Q→03[4 marks sum]
26 Q→04[5 marks sum]
17 Q→05MCQ
40 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 given figure, the sides BA and CA of $\triangle ABC$ have been produced to D and E such that $BA = AD$ and $CA = AE$. Prove that, $ED \| BC$.
View full solution →AB is a line segment. AX and BY are two equal line segments drawn on opposite sides of $A B$ such that $A X \| Y B$. If $A B$ and $X Y$ intersect at $M$, prove that :
(i) $\triangle AMX \cong \triangle BMY$
(ii) AB and XY bisect each other at M .
View full solution →(i) $\triangle AMX \cong \triangle BMY$
(ii) AB and XY bisect each other at M .
In the given figure, $PA \perp AB ; QB \perp AB$ and $PA = QB$. If PQ intersects AB at M , show that M is the mid-point of both AB and PQ .
View full solution →In the given figure, $M$ is the mid-point of $A B$ and $C D$. Prove that $CA = BD$ and $CA \| BD$.
View full solution →In the adjoining figure, $AB > AC$ and D is any point on BC. Show that : $AB > AD$.
View full solution →In the given figure, $AB > AC$. If BO and CO are the bisectors of $\angle B$ and $\angle C$ respectively, prove that $BO > CO$.
View full solution →In the given figure, AD bisects $\angle A$. If $\angle B =60^{\circ}, \angle C =$ $40^{\circ}$, then arrange $AB , BD$ and DC in ascending order of their lengths.
View full solution →The sides AB and AC of $\triangle ABC$ are produced to D and E respectively and the bisectors of $\angle CBD$ and $\angle BCE$ meet at O . If $AB > AC$, prove that $OC > OB$.
View full solution →In the adjoining figure, $\triangle ABC$ is equilateral and D is any point on AC.
Prove that :
(i) $BD > AD$
(ii) $BD > DC$.
View full solution →Prove that :
(i) $BD > AD$
(ii) $BD > DC$.
In the given figure, sides AB and AC of $\triangle ABC$ have been produced to D and E respectively. If $\angle CBD =x^{\circ}$ and $\angle BCE$ $=y^{\circ}$ such that $x>y$, show that $AB > AC$.
View full solution →In a right-angled triangle, prove that the hypotenuse is the longest side.
In the given figure, side $A B$ of $\triangle A B C$ is produced to $D$ such that $BD = BC$.
If $\angle A =60^{\circ}$ and $\angle B =50^{\circ}$, prove that :
(i) $AD > CD$
(ii) $AD > AC$.
View full solution →If $\angle A =60^{\circ}$ and $\angle B =50^{\circ}$, prove that :
(i) $AD > CD$
(ii) $AD > AC$.
In the given figure, $\angle ABC =66^{\circ}, \angle DAC =38^{\circ}$. CE is perpendicular to AB and AD is perpendicular to BC .
Prove that: $CP > AP$.
View full solution →Prove that: $CP > AP$.
In $\triangle ABC , AB =7.5 cm, BC =6.2 cm$ and $AC =5.4 cm$. Name :
(i) the least angle
(ii) the greatest angle of the triangle.
View full solution →(i) the least angle
(ii) the greatest angle of the triangle.
In the adjoining figure, $AC > AB$ and AD is the bisector of $\angle A$. Show that: $\angle ADC >\angle ADB$.
View full solution →In the given figure, $AB = AC$. Show that $AD > AB$.
View full solution →In the given figure, $AD = AB$ and AE bisects $\angle A$.
Prove that :
(i) $BE = ED$
(ii) $\angle ABD >\angle BCA$.
View full solution →Prove that :
(i) $BE = ED$
(ii) $\angle ABD >\angle BCA$.
If O is any point inside $\triangle ABC$, prove that $\angle BOC >\angle A$.
View full solution →In the adjoining quadrilateral $ABCD , AB$ is the longest side and DC is the shortest side. Prove that :
(i) $\angle C >\angle A$
(ii) $\angle D >\angle B$.
View full solution →(i) $\angle C >\angle A$
(ii) $\angle D >\angle B$.
The lengths of the three sides of a triangle are $4 cm, 5 cm$ and 7 cm . Which of the following cannot be the length of any one of the medians?
- A2.5 cm
- B3.8 cm
- C5 cm
- ✓none of these
Answer: D.
View full solution →ABD is a triangle such that $\angle ADB =20^{\circ}$ and C is a point on BD such that $AB =$ AC and $CD = CA$. The measure of $\angle ABC$ is :
- ✓$40^{\circ}$
- B$50^{\circ}$
- C$55^{\circ}$
- D$60^{\circ}$
Answer: A.
View full solution →ABC is a triangle in which $AC = BC$ and $\angle BAC =50^{\circ}$. Side BC is produced to D such that $BC = CD . \angle BAD$ is equal to :
- A$45^{\circ}$
- B$50^{\circ}$
- ✓$90^{\circ}$
- D$100^{\circ}$
Answer: C.
View full solution →In the figure, $\triangle ABD \cong \triangle ACD$. If $\angle DAC =30^{\circ}$ and $\angle BDC =110^{\circ}$, then the measure of $\angle DBA$ is :
- A$30^{\circ}$
- B$50^{\circ}$
- C$70^{\circ}$
- ✓$25^{\circ}$
Answer: D.
View full solution →In the given figure, the bisectors of $\angle B$ and $\angle C$ intersect each other at O and $\angle BAC =50^{\circ}$. The measure of $\angle BOC$ is :
- A$100^{\circ}$
- ✓$115^{\circ}$
- C$130^{\circ}$
- D$140^{\circ}$
Answer: B.
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