Which of the following is the set of measures of the sides of a triangle?
- A$8\ cm, 4\ cm, 20\ cm$
- ✓$9\ cm, 17\ cm, 25\ cm$
- C$11\ cm, 16\ cm, 28\ cm$
- DNone of these.
Answer: B.
View full solution →Question types
The Triangles and Its Properties question types
319 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
319
Questions
9
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
191 Q→02Assertion (A) & Reason (B) MCQ
15 Q→03True False[1 Marks ]
19 Q→04BLANKS [1 Marks Each]
30 Q→051 Marks Question
12 Q→062 Marks Questions
20 Q→075 Marks Questions
4 Q→08case /data -based (4 Marks)
7 Q→093 Marks Question
21 Q→Sample Questions
The Triangles and Its Properties questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The top of a broken tree touches the ground at a distance of $12m$ from its base. If the tree is broken at a height of $5m$ from the ground then the actual height of the tree is:
- A$25m$
- B$13m$
- ✓$18m$
- D$17m$
Answer: C.
View full solution →Which of the following is$/$ are not Pythagorean triplet $(s)?$
- A$3, 4, 5$
- B$8, 15, 17$
- C$7, 24, 25$
- ✓$13, 26, 29$
Answer: D.
View full solution →Find the value of $x$ in the adjoining figure.
- A$50^\circ$
- ✓$120^\circ$
- C$60^\circ$
- D$70^\circ$
Answer: B.
View full solution →Vikash wants to plant a flower on the ground in the form of a rhombus. The diagonals of the rhombus measure $42\ cm$ and $56\ cm.$ Find the perimeter of the field.
- A$150\ cm$
- ✓$140\ cm$
- C$130\ cm$
- D$120\ cm$
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 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 $3.4$
Reason: the difference between the two sides of a triangle should be less than the third side.
Assertion: 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 $3.4$
Reason: the difference between the two sides of a triangle should be less than the third side.
- ✓Both Assertion and reason are correct and reason is correct explanation for Assertion.
- BBoth Assertion and reason are correct but reason is not correct explanation for Assertion.
- CAssertion is true but reason is false.
- DBoth Assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In congruent triangle corresponding part are equal.
Reason: Two triangles are congruent if any two pairs of angle and pairs of corresponding sides are equal
Assertion: In congruent triangle corresponding part are equal.
Reason: Two triangles are congruent if any two pairs of angle and pairs of corresponding sides are equal
- ABoth Assertion and reason are correct and reason is correct explanation for Assertion.
- ✓Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- CAssertion is true but reason is false.
- DBoth Assertion and reason are false.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If the sides of a triangle are $9\ cm, 13\ cm$ and $14\ cm. 36$ its perimeter
Reason: perimeter of triangle $= a + b + c$
Assertion: If the sides of a triangle are $9\ cm, 13\ cm$ and $14\ cm. 36$ its perimeter
Reason: perimeter of triangle $= a + b + c$
- ✓Both Assertion and reason are correct and reason is correct explanation for Assertion.
- BBoth Assertion and reason are correct but reason is not correct explanation for Assertion.
- CAssertion is true but reason is false.
- DBoth Assertion and reason are false.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Two angles measures $a - 60^\circ $ and $123^\circ - 2a$. If each one is opposite to equal sides of an isosceles triangle, then the value of a is $61^\circ $.
Reason: Sides opposite to equal angles of a triangle are equal.
Assertion: Two angles measures $a - 60^\circ $ and $123^\circ - 2a$. If each one is opposite to equal sides of an isosceles triangle, then the value of a is $61^\circ $.
Reason: Sides opposite to equal angles of a triangle are equal.
- ABoth Assertion and reason are correct and reason is correct explanation for Assertion.
- ✓Both Assertion and reason are correct but reason is not correct explanation for Assertion.
- CAssertion is true but reason is false.
- DBoth Assertion and reason are false.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $ABC$ is an equilateral triangle, then each angle equals to $60^\circ $
Reason: Equilateral triangle has all its sides equal and each angle measures $60^\circ $.
Assertion: $ABC$ is an equilateral triangle, then each angle equals to $60^\circ $
Reason: Equilateral triangle has all its sides equal and each angle measures $60^\circ $.
- ✓Both Assertion and reason are correct and reason is correct explanation for Assertion.
- BBoth Assertion and reason are correct but reason is not correct explanation for Assertion.
- CAssertion is true but reason is false.
- DBoth Assertion and reason are false.
Answer: A.
View full solution →In $\triangle ABC , AB + BC > AC$.
View full solution →In $\triangle PQR , \angle P =\angle Q =60^{\circ}$, then $\overline{ PR }$ is the longest side.
View full solution →We can have an acute, an obtuse and a right angle in a triangle.
In $\triangle XYZ , \angle Z =90^{\circ}$, then $\angle X +\angle Y =90^{\circ}$.
View full solution →In $\triangle PQR , \angle Q =90^{\circ}$, therefore $\overline{ PR }$ is the hypotenuse.
View full solution →Two angles of a triangle are $60^{\circ}$, then the triangle is…………(right-angled, scalene, equilateral)
View full solution →A ladder of length $5 m$ is resting on the top of a wall of height $4 m$.The distance of the ladder from the wall must be………..$m. (3. 4. 5)$
View full solution →$\triangle ABC$ is right-angled at $C$. If $AC =5$ and $AB =13$, then $B C=………… (12. 13. 18)$
View full solution →A/An………...-angled triangle may be scalene, isosceles or equilateral. (acute, obtuse, right)
In $\triangle ACB , \angle C =90^{\circ}$, then is the hypotenuse. $(\overline{A B}, \overline{B C}, \overline{C A})$
View full solution →Are these be the sides of a right triangle? In the case of right-angled triangles, identify the right angle.
$1.5 \ cm, 2 \ cm, 2.5 \ cm.$
View full solution →$1.5 \ cm, 2 \ cm, 2.5 \ cm.$
Which of the following can be the sides of a right-angled triangle? $2 \ cm, 2\ cm, 5 \ cm$
View full solution →Are these be the sides of a right triangle? In the case of right-angled triangles, identify the right angle.
$2.5 \ cm, 6.5 \ cm, 6 \ cm$
View full solution →$2.5 \ cm, 6.5 \ cm, 6 \ cm$
In $\triangle$ PQR the following figure, $D$ is the mid-point of $QR$, is $QM = MR?$
View full solution →In $\triangle PQR$ the adjoining figure, $D$ is the mid-point of $QR. PD$ is ________.
View full solution →The diagonals of a rhombus measure $16 \ cm$ and $30 \ cm$. Find its perimeter.
View full solution →Find the perimeter of the rectangle whose length is $40 \ cm$ and a diagonal is $41 \ cm.$
View full solution →Angles $Q$ and $R$ of a $\triangle PQR$ are $25^\circ $ and $65^\circ $. Write which of the following is true:
View full solution →A tree is broken at a height of $5 \ m$ from the ground and its top touches the ground at a distance of $12 \ m$ from the base of the tree. Find the original height of the tree.
View full solution →A $15 \ m$ long ladder reached a window $12 \ m$ high from the ground on placing it against a wall at distance a. Find the distance of the foot of the ladder from the wall.
View full solution →The lengths of two sides of a triangle are $12 \ cm$ and $15 \ cm$. Between what two measures should the length of the third side fall?
View full solution →$ABCD$ is a quadrilateral. Is $AB + BC + CD + DA < 2(AC + BD) ?$
View full solution →$ABCD$ is a quadrilateral. Is $AB + BC + CD + DA > AC + BD?$
View full solution →Verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same.
In the triangle $ABC$ below, $AC = BC.$ In the triangle $DCE, \angle CED = 90^\circ .$
$1$.What is the value of $'x\ ’?$
$1$.What is the value of $'x\ ’?$
- A$40$
- ✓$50$
- C$60$
- D$70$
Answer: B.
View full solution →In the triangle $XYZ,$ the median $XP$ is half the length of the side $YZ.$
In the triangle, $XZQ, XZ = ZQ.$
$1.$ What is the measure of $\angle ZXQ?$
View full solution →In the triangle, $XZQ, XZ = ZQ.$
$1.$ What is the measure of $\angle ZXQ?$
A shelf with a triangular frame is ixed on a wall as shown below.
The lengths of the rods used in the shaded triangular frame are $48\ cm, 55\ cm$ and $73\ cm.$
$1.$ What is the type of the shaded triangle$?$
$A.$ Obtuse triangle
$B.$ Isosceles triangle
$C.$ Equilateral triangle
$D. $ Right-angled triangle
$2.$ What can be the height of the shelf$?$
View full solution →The lengths of the rods used in the shaded triangular frame are $48\ cm, 55\ cm$ and $73\ cm.$
$1.$ What is the type of the shaded triangle$?$
$A.$ Obtuse triangle
$B.$ Isosceles triangle
$C.$ Equilateral triangle
$D. $ Right-angled triangle
$2.$ What can be the height of the shelf$?$
In the figure shown below, $PQR$ is a straight line.
The measure of $\angle PXQ = 20^\circ .$
$1.$ What is the measure of $\angle PXR?$
View full solution →The measure of $\angle PXQ = 20^\circ .$
$1.$ What is the measure of $\angle PXR?$
Pratibha made a paper lag by pasting an isosceles right triangle on a stick.
$1.$ What is the measure of $\angle ACD?$
View full solution →$1.$ What is the measure of $\angle ACD?$
$AM$ is a median of a triangle $ABC.$
Is $AB + BC + CA > 2 AM?($Consider the sides of triangles $\triangle ABM$ and $\triangle AMC.)$
View full solution →Is $AB + BC + CA > 2 AM?($Consider the sides of triangles $\triangle ABM$ and $\triangle AMC.)$
Take any point $O$ in the interior of a triangle $PQR.$ Is $OR + OP > RP?$
View full solution →Take any point $O$ in the interior of a triangle $PQR.$ Is $OQ + OR > QR?$
View full solution →Take any point $O$ in the interior of a triangle $PQR.$ Is $OP + OQ > PQ?$
View full solution →Is it possible to have a triangle with the sides $6\ cm, 3\ cm, 2\ cm$
View full solution →Generate a The Triangles and Its Properties paper free
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