Previous Year Questions: Triangles

# Previous Year Questions: Triangles | Mathematics (Maths) Class 10 PDF Download

 Table of contents Previous Year Questions 2024 Previous Year Questions 2023 Previous Year Questions 2022 Previous Year Questions 2021 Previous Year Questions 2020 Previous Year Questions 2019

## Previous Year Questions 2024

Q1: In ΔABC, DE || BC (as shown in the figure). If AD = 2 cm, BD = 3 cm, BC = 7.5 cm, then the length of DE (in cm) is:     (2024)
(a) 2.5
(b) 3
(c) 5
(d) 6

Ans: (b)

Q2: In ΔABC, if AD ⊥ BC and AD2 = BD × DC, then prove that ∠BAC = 90º.       (2024)

Ans:

Here,

and
and ∠ADB = ∠CDA [Each 90°]
∠1 = ∠2 [By CPST]
∠3 = ∠4 (i)
∠3 + ∠ADC + ∠1 = 180°
∠3 + 90° + ∠1 = 180°
∠1 = 180° – 90° – ∠3
∠1 = 90° – ∠3
∠BAC = ∠1 + ∠4
= 90° – ∠3 + ∠3
[∵∠4 = ∠3 From eqn. (i)]
i.e., ∠BAC = 90°
Hence, Proved

## Previous Year Questions 2023

Q3: in ΔABC, PQ || BC If PB = 6 cm, AP = 4 cm, AQ = 8 cm. find the length of AC.   (2023)
(a ) 12 cm
(b) 20 cm
(c) 6 cm
(d) 14 cm

Ans: (b)
Sol: Since, PQ || BC
[By Thales theorem]

= 12 cm

Q4: In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC = 2 cm, BM = 3 cm and MC = 5 cm. Find the length of XY.   (2023)

Ans: Given, AZ = 3 cm, ZC = 2 cm. BM = 3 cm and MC = 5 cm
In ΔABC, XZ || BC

Now, AC = AZ + ZC = 3 + 2 = 5cm
BC = BM + MC = 3 + 5 = 8 cm and
In ΔAXY and ΔABM
∠AXY = ∠ABM (Corresponding angles are equal as XZ || BC)
∠XAY = ∠BAM (Common)
∴ ΔAXY ∼ ΔABM (By AA similarity criterion)

(Corresponding sides of similar triangles)
From (i) and (ii), we get

= 1.8cm

Q5: Assertion (A) : The perimeter of ΔABC is a rational number.
Reason (R) : The sum of the squares of two rational numbers is always rational.   (2023)

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

Ans: (d)

In ΔABC, AC2 = AB2 + BC2
⇒ AC2 = 22 + 32
⇒ AC2 = 4 + 9
⇒ AC= √13 cm
So, perimeter is (2 + 3 + √13)cm = (5 + √13), which is irrational.
Hence, Assertion in false but Reason is true.

## Previous Year Questions 2022

Q6: In the figure given below, what value of x will make PQ || AB?    (2022)

(a) 2
(b) 3
(c) 4
(d) 5

Ans: (a)
Sol: Suppose PQ || AB
By Basic Proportionality theorem we have

⇒ 6x = 12
⇒ x = 2
So, for x = 2, PQ IIAB

Q7: If Δ ABC and Δ PQR are similar triangles such that ∠A = 31° and ∠R = 69°, then ∠Q is :    (2022)
(a) 70°
(b) 100°
(c) 90°
(d) 80°

Ans: (d)
Sol: Given Δ ABC and Δ PQR are similar.

Hence, ∠A = ∠P, ∠B = ∠Q and ∠C = ∠R
We know that,
∠P + ∠Q + ∠R = 180°
31° + ∠Q + 69° = 180°
100° + ∠Q = 180°
∠Q = 180° - 100°
∠Q = 80°

Q8: A vertical pole of length 19 m casts a shadow 57 m long on the ground and at the same time a tower casts a shadow 51m long. The height of the tower is    (2022)
(a) 171m
(b) 13 m
(c) 17 m
(d) 117 m

Ans: (c)
Sol: Let AB be the pole and PQ be the tower
Let height of tower be h m
Now, ΔABC ∼ ΔPQR

⇒ h = 17m

## Previous Year Questions 2021

Q9: Aman goes 5 metres due west and then 12 metres due North. How far is he from the starting point?    (2021)

Ans: 13 m
Let Aman starts from A point and continues 5 m towards west and readied at B point, from which he goes 12 m towards North reached at C point finally.
In ΔABC, we have

AC2 = AB2 + BC2              [By Pythagoras theorem]
AC2 = 52 + 122
AC2 = 25 + 144 = 169
AC = 13m
So, Aman is 13 m away from his starting point.

## Previous Year Questions 2020

Q10: All concentric circles are ___________ to each other.    (2020)

Ans: All concentric circles arc similar to each other.

Q11: In figure, PQ || BC, PQ = 3 cm, BC = 9 cm and AC = 7.5 cm. Find the length of AQ.    (2020)

Ans: Given, PQIIBC
PQ = 3 cm, BC = 9 cm and AC = 7.5 cm
Since. PQ || BC
∴ ∠APQ = ∠ABC (Corresponding angles are equal)
Now,  in ΔAPQ and ΔABC
∠APQ =∠ABC        (Corresponding angles are equal)
∠A = ∠A                  (Common)
ΔAPQ ∼ ΔABC    (AA similarity)

## Previous Year Questions 2019

Q12: In figure, GC||BD and GE||BF. If AC = 3cm and CD = 7 cm, then find the value of AE / AF.    (2019)

Ans: 3/10
Here in the given figure.
GC || BD and GE || BF
AC = 3 cm and CD = 7 cm
By Basic Proportionality theorem.

We get,

Q13: The perpendicular from A on the side BC of a ΔABC intersects BC at D, such that DB = 3CD. Prove that 2AB2 = 2AC2 + BC2.    (2019)

Ans: We have, ΔABC such that AD⊥BC. ΔABC Intersect SC at D such that BD = 3CD.
In right ΔADB, by Pythagoras theorem, we have
AB2 = AD2  +  BD2    _(i)
Similarly in ΔACD, we have AC2 = AD2 +CD2    _(ii)
Subtracting (ii) from (i), we get
AB- AC2 = BD2 - CD2    _(iii)
Now, BC = DB + CD = 4CD    [∵ BD = 3CD]

Substituting the value of BD and CD in eqn.(iii) we get

Hence proved.

The document Previous Year Questions: Triangles | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## Mathematics (Maths) Class 10

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## FAQs on Previous Year Questions: Triangles - Mathematics (Maths) Class 10

 1. How do you calculate the area of a triangle?
Ans. To calculate the area of a triangle, you can use the formula: Area = 1/2 * base * height. Simply multiply the base of the triangle by the height of the triangle, and then divide that number by 2.
 2. What is the Pythagorean Theorem and how is it used in triangles?
Ans. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem is commonly used to find missing side lengths in right triangles.
 3. How do you determine if three given side lengths form a triangle?
Ans. To determine if three given side lengths form a triangle, you can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is satisfied for all three combinations of sides, then the given lengths form a triangle.
 4. What are the different types of triangles based on their angles?
Ans. There are three main types of triangles based on their angles: acute triangles (all angles are less than 90 degrees), obtuse triangles (one angle is greater than 90 degrees), and right triangles (one angle is exactly 90 degrees).
 5. How can you find the missing angle in a triangle?
Ans. To find the missing angle in a triangle, you can use the fact that the sum of the three angles in any triangle is always 180 degrees. Simply subtract the measurements of the two known angles from 180 degrees to find the measure of the missing angle.

## Mathematics (Maths) Class 10

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