Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Previous Year Questions: Triangles

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

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)
Previous Year Questions: Triangles | Mathematics (Maths) Class 10(a) 2.5
(b) 3
(c) 5
(d) 6

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: (b) 
Previous Year Questions: Triangles | Mathematics (Maths) Class 10In ΔABC, DE || BC 
AD = 2 cm 
BD = 3 cm
∴ AB = AB + BD
= (2 + 3) cm 
AB = 5 cm 
Now, ∠ADE = ∠ABC, ∠AED = ∠ACB [Corresponding angles] 
So by AA prop. ΔADE ∼ ΔABC
⇒ AD/AB = DE/BC
⇒ 2/5 = DE/7.5
DE = 3 cm


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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans:
Previous Year Questions: Triangles | Mathematics (Maths) Class 10

Here,
AD ⊥ BC

and
AD2 = BD × DC
i.e., AD × AD = BD × DC
AD/DC = BD/AD
and ∠ADB = ∠CDA [Each 90°]
⇒ ∆ADB ~ ∆CDA
∠1 = ∠2 [By CPST]
∠3 = ∠4 (i)
In ∆AD C,
∠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)
Previous Year Questions: Triangles | Mathematics (Maths) Class 10(a ) 12 cm 
(b) 20 cm 
(c) 6 cm 
(d) 14 cm

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: (b)
Sol: Since, PQ || BC
∴ Previous Year Questions: Triangles | Mathematics (Maths) Class 10 [By Thales theorem]
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
= 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)
Previous Year Questions: Triangles | Mathematics (Maths) Class 10

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: Given, AZ = 3 cm, ZC = 2 cm. BM = 3 cm and MC = 5 cm
In ΔABC, XZ || BC
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
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)
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
(Corresponding sides of similar triangles)
From (i) and (ii), we get
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
= 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)
Previous Year Questions: Triangles | Mathematics (Maths) Class 10

(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. 

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: (d)

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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10(a) 2
(b) 3
(c) 4
(d) 5

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: (a)
Sol: Suppose PQ || AB
By Basic Proportionality theorem we have
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
⇒ 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°

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: (d)
Sol: Given Δ ABC and Δ PQR are similar.
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

Ans: (c)
Sol: Let AB be the pole and PQ be the tower
Let height of tower be h m
Now, ΔABC ∼ ΔPQR
Previous Year Questions: Triangles | Mathematics (Maths) Class 10
⇒ 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)

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

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

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)

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

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: Triangles | Mathematics (Maths) Class 10


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)

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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10
We get, Previous Year Questions: Triangles | Mathematics (Maths) Class 10

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


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

Previous Year Questions: Triangles | Mathematics (Maths) Class 10  View Answer

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]

Previous Year Questions: Triangles | Mathematics (Maths) Class 10
Substituting the value of BD and CD in eqn.(iii) we get
Previous Year Questions: Triangles | Mathematics (Maths) Class 10

Hence proved.

The document Previous Year Questions: Triangles | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10
124 videos|457 docs|77 tests

Top Courses for Class 10

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

1. What are the different types of triangles based on their sides?
Ans.Triangles can be classified based on their sides into three types: equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), and scalene triangles (all sides are of different lengths).
2. How do you find the area of a triangle?
Ans.The area of a triangle can be calculated using the formula: Area = (base × height) / 2. Here, the base is any side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.
3. What is the Pythagorean theorem and how is it related to right triangles?
Ans.The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is expressed as a² + b² = c².
4. How can the angles of a triangle be determined?
Ans.The sum of the interior angles of a triangle is always 180 degrees. If two angles are known, the third angle can be found by subtracting the sum of the two known angles from 180 degrees.
5. What is the significance of the triangle inequality theorem?
Ans.The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This theorem is essential for determining whether three given lengths can form a triangle.
124 videos|457 docs|77 tests
Download as PDF
Explore Courses for Class 10 exam

Top Courses for Class 10

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

study material

,

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

,

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

,

Summary

,

Viva Questions

,

practice quizzes

,

shortcuts and tricks

,

past year papers

,

pdf

,

Free

,

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

,

Extra Questions

,

Semester Notes

,

video lectures

,

Exam

,

mock tests for examination

,

Objective type Questions

,

Important questions

,

Previous Year Questions with Solutions

,

Sample Paper

,

MCQs

,

ppt

;