Find the length of the diagonal of a rectangle whose sides are 21 cm and 20 cm .
Question types
Properties of Triangles question types
93 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
93
Questions
7
Question groups
5
Question types
01
[1 Mark Question Answer]
18 Q→02[2 Mark Question Answer]
31 Q→03[3 marks sum]
10 Q→04[4 marks sum]
3 Q→05TRUE / FALSE
5 Q→06Fill in the blanks.
8 Q→07MCQ
18 Q→Sample Questions
Properties of Triangles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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In a right-angled triangle, the two acute angles are in the ratio $4: 5$. Find these angles.
View full solution →One angle of a triangle measures $30^{\circ}$ and the other two angles are in the ratio $3: 2$. Find these angles.
View full solution →The angles of a triangle are in the ratio $3: 5: 4$. Find the measure of each of the angles.
View full solution →In a $\triangle PQR$, if $\angle P =90^{\circ}$ and $\angle Q =\angle R$, find the measure of each of the equal angles of the triangle.
View full solution →A long pole is made to stand against a wall in such a way that its foot is 16 m from the wall and its top reaches a window 12 m above the ground. Find the length of the pole.
A man travels 90 km due East and then 56 km due South. How far is he from the starting point?
The two legs of a right triangle are equal and the square of its hypotenuse is 50 cm . Find the length of each leg.
The length of one side of a right triangle is 24 cm and the length of its hypotenuse is 40 cm . Find the length of its third side.
In a right angled triangle, find the length of the hypotenuse, if the other two sides measure 12 cm and 35 cm .
Given below are the lengths of the sides of $\triangle A B C$. In each case, state whether $\triangle A B C$ is right angled or not :
(i) $AB =40 cm, BC =58 cm, CA =44 cm$
(ii) $AB =43 cm, BC =35 cm, CA =12 cm$
(iii) $AB =55 cm, BC =73 cm, CA =48 cm$
View full solution →(i) $AB =40 cm, BC =58 cm, CA =44 cm$
(ii) $AB =43 cm, BC =35 cm, CA =12 cm$
(iii) $AB =55 cm, BC =73 cm, CA =48 cm$
Given below are the lengths of the legs of right $\triangle A B C$. In each case, find the length of the hypotenuse of $\triangle A B C$ :
(i) $a=32 cm, b=60 cm$
(ii) $a=28 m, b=45 m$
(iii) $a=32 cm, b=24 cm$
View full solution →(i) $a=32 cm, b=60 cm$
(ii) $a=28 m, b=45 m$
(iii) $a=32 cm, b=24 cm$
In the given figure, $\triangle ABC$ is an isosceles triangle in which $AB = AC$ and $\angle A =50^{\circ}$. Find the measure of $\angle B$ and $\angle C$.
View full solution →In the figure, one side of a triangle has been produced. Find all the angles of the triangle in :
State Pythagoras' Theorem.
In the given figure, $\triangle ABC$ is an equilateral triangle whose side BC has been produced in both the directions to D and E respectively. Prove that $\angle ACD =\angle ABE$.
View full solution →Use the given figure to express:
(i) $a$ in terms of $b$ and $f$;
(ii) $e$ in terms of $f$ and $g$;
(iii) $d$ in terms of $a$ and $e$;
(iv) $c$ in terms of $e$ and $g$.
View full solution →(i) $a$ in terms of $b$ and $f$;
(ii) $e$ in terms of $f$ and $g$;
(iii) $d$ in terms of $a$ and $e$;
(iv) $c$ in terms of $e$ and $g$.
The sum of two acute angles of a right angled triangle is $45^{\circ}$.
View full solution →A triangle having two of its angles measuring $30^{\circ}$ and $70^{\circ}$ is scalene.
View full solution →In a right triangle ABC , if $AC ^2+ AB ^2= BC ^2$, then the right angle is $\angle B$.
View full solution →A triangle can have all the three angles less than $60^{\circ}$.
View full solution →A triangle can have at most two angles greater than $90^{\circ}$.
View full solution →If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is __________.
The sum of the two acute angles in a right angled triangle is __________.
If two angles of a triangle are $36^{\circ}$ and $63^{\circ}$, then the third angle is _________.
View full solution →The longest side of a right angled triangle is _________.
In a scalene triangle the measures of all the three angles are _________.
A 15 m long ladder is rested against a wall such that the foot of the ladder is 12 m away from the wall. How up on the wall is the upper end of the ladder?
- A6 m
- B8 m
- ✓9 m
- D10 m
Answer: C.
View full solution →Which of the following cannot be the sides of a right angled triangle?
- A5 cm, 4 cm, 3 cm
- B12 cm, 5 cm, 13 cm
- ✓15 cm, 21 cm, 27 cm
- D37 cm, 35 cm, 12 cm
Answer: C.
View full solution →In the given figure, find the value of x.
- A7
- B9
- ✓11
- D13
Answer: C.
View full solution →Find the value of x in the given figure.
- A$25^{\circ}$
- B$30^{\circ}$
- ✓$35^{\circ}$
- D$45^{\circ}$
Answer: C.
View full solution →A triangle can have two
- Astraight angles
- Bobtuse angles
- Cright angles
- ✓acute angles
Answer: D.
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