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In our daily lives, we can observe that some traffic signal sign boards, a slice of pizza, are in the shape of a triangle, i.e. they all have three sides. In the NCERT Exemplar Class 9 Chapter 7, Triangles, we will deep dive into the world of triangles, exploring the properties of triangles, and some important theorems related to triangles, like Pythagoras' theorem and the congruence theorems etc. This chapter is all about understanding how triangles form the foundation of geometry and are used in real-world structures around you.
This article on NCERT Exemplar Class 9 Maths Solution Chapter 7, Triangles, offers clear and step-by-step solutions for the exercise problems in the NCERT Exemplar Class 9 Maths book. Students who are in need of the Triangles class 9 exemplar solutions will find this article very useful. It covers all the important Class 9 Maths Chapter 7 question answers. These Triangles class 9 ncert exemplar solutions are made by the Subject Matter Experts according to the latest CBSE syllabus, ensuring that students can grasp the basic concepts effectively. For the NCERT syllabus, books, notes, and class-wise solutions, refer to the NCERT.
NCERT Exemplar Class 9 Maths Solutions Chapter 7: Exercise 7.1 Page: 64, Total Questions: 11 |
Question:1
Which of the following is not a criterion for the congruence of triangles?
(A) SAS
(B) ASA
(C) SSA
(D) SSS
Answer:
[C] SSA is correct optionQuestion:2
If AB = QR, BC = PR and CA = PQ, then
(A)△ABC≅△PQR(B)△CBA≅△PRQ(C)△BAC≅△RPQ(D)△PQR≅△BCA
Answer:
[B]Question:3
In △ABC, AB = AC and ∠B=50∘. Then ∠C is equal to
(A)40∘(B)50∘(C)80∘(D)130∘
Answer:
[B] Solution.Question:4
In △ABC, BC = AB and ∠B = 80∘. Then ∠A is equal to
(A)80∘(B)40∘(C)50∘(D)100∘
Answer:
[C]Question:5
In △PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is
(A) 4 cm
(B) 5 cm
(C) 2 cm
(D) 2.5 cm
Answer:
[A]Question:6
D is a point on the side BC of a △ABC such that AD bisects ∠BAC. Then
(A) BD = CD
(B) BA > BD
(C) BD > BA
(D) CD > CA
Answer:
[A]Question:7
It is given that △ABC ≅ △FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
(A) DF = 5 cm, ∠F = 60°
(B) DF = 5 cm, ∠E = 60°
(C) DE = 5 cm, ∠E = 60°
(D) DE = 5 cm, ∠D = 40°
Answer:
[B]Question:8
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
(A) 3.6 cm
(B) 4.1 cm
(C) 3.8 cm
(D) 3.4 cm
Answer:
[D]Question:9
In △PQR, if ∠R > ∠Q, then
(A) QR > PR
(B) PQ > PR
(C) PQ < PR
(D) QR < PR
Answer:
[B]Question:10
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B =∠Q. The two triangles are
(A) isosceles but not congruent
(B) isosceles and congruent
(C) congruent but not isosceles
(D) neither congruent nor isosceles
Answer:
[A]NCERT Exemplar Class 9 Maths Solutions Chapter 7: Exercise 7.2 Page: 65-66, Total Questions: 12 |
Question:1
Answer:
Given : In triangles ABC and PQR, ∠A = ∠Q and∠B =∠RQuestion:2
Answer:
Side BC should be equal to side PR.Question:3
Answer:
If two sides and the included angle of one triangle are equal to the two side and the included angle of the other triangle then only the triangles can be congruent by SAS criterion of congruence otherwise not.Question:4
Answer:
[True]Question:5
Answer:
Not possible.Question:7
If △PQR≅ △EDF, then is it true to say that PR = EF? Give reason for your answer.
Answer:
TrueQuestion:8
Answer:
[PR]Question:9
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD?
Give reason for your answer.
Answer:
TrueQuestion:10
Answer:
TrueQuestion:11
Answer:
[Not possible]Question:12
Answer:
YesNCERT Exemplar Class 9 Maths Solutions Chapter 7: Exercise 7.3 Page: 67-68, Total Questions: 11 |
Question:4
In Figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that △ABC ≅ △DEF.
Answer:
Given, BA ⊥ ACQuestion:5
Q is a point on the side SR of a DPSR such that PQ = PR. Prove that PS > PQ.
Answer:
Given: Q is point on side SR in DPSR and PQ = PRQuestion:6
S is any point on side QR of a △PQR. Show that:PQ + QR + RP > 2 PS.
Answer:
Given, △PQR, S is any point on QR.Question:7
D is any point on side AC of a △ABC with AB = AC. Show that CD < BD.
Answer:
Given: ABC is a triangle and D is any point on AC.Question:8
Answer:
Given : l∥mQuestion:9
Answer:
Given: ABC is a isosceles triangle AB = ACQuestion:10
Answer:
Given, ABC is an isosceles triangleQuestion:11
In given figure, AD is the bisector of ∠BAC. Prove that AB > BD.
Answer:
Given: In △ABC, AD is bisector of ∠BAC.NCERT Exemplar Class 9 Maths Solutions Chapter 7: Exercise 7.4 Page: 69-71, Total Questions: 21 |
Question:1
Find all the angles of an equilateral triangle.
Answer:
[60∘]Question:2
Answer:
Given : ABC is an triangle and let O is a point on AB.Question:3
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In △ABD and △ACD,
AB = AC (Given)
∠B = ∠C (because AB = AC)
and ∠ADB = ∠ADC
Therefore, △ABD ≅ △ACD (AAS)
So, ∠BAD =∠CAD (CPCT)
What is the defect in the above arguments?
Answer:
[∠ABD = ACD is defect.]Question:4
Answer:
Given : P is a point on the bisector at ÐABC.Question:5
Answer:
Given: ABCD is a quadrilateral in which AB = BC and AD = CDQuestion:6
ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2 AD.
Answer:
Given : ABC is a right triangle AB = ACQuestion:7
Answer:
ABCD is square. O is any interior point of the square and OAB is an equilateral triangle.Question:8
Answer:
Question:9
Answer:
Given: △ABC is isosceles triangle AB = ACQuestion:10
Answer:
Question:11
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2 (BD + AC)
Answer:
Given : ABCD is a quadrilateralQuestion:12
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
Answer:
Given, ABCD is a quadrilateralQuestion:13
Answer:
ABC is triangle and D is mid-point at ACQuestion:14
Answer:
Given : ABC is right angle triangleQuestion:15
Answer:
Given: l and m intersect at point O and P is a point on a line n passing through O andQuestion:16
Answer:
Given : ABCD is trapeziumQuestion:17
Answer:
Given: ABCD is quadrilateralQuestion:18
Answer:
Given, ABC is right angle triangleQuestion:19
Answer:
ABCD is quadrilateralQuestion:20
Answer:
Given: ABC is triangle and AC is longest sideSalient topics covered in the NCERT exemplar Class 9 Maths solutions chapter 7 are mentioned below:
These NCERT exemplar problems are very useful for students as they go beyond the basics, helping students grasp more advanced concepts with greater clarity.
Given below are the subject-wise exemplar solutions of class 9 NCERT:
Here are the subject-wise links for the NCERT solutions of class 9:
Given below are the subject-wise NCERT Notes of class 9:
Here are some useful links for NCERT books and the NCERT syllabus for class 9:
If two triangles are similar, their corresponding interior angles will be the same; however, the side length will not be the same. If two triangles are congruent, then their corresponding angles and side-lengths will be the same.
No, it is not possible to make a triangle with these three side lengths. Sum of two sides must be more than the third side length.
As, 5 + 8 <14
Therefore, 5,8, and 14 cannot be the sides of a triangle.
If two triangles are congruent, they will have the same interior angles and the same sides. Therefore, they must be similar, and however, if two triangles are similar, they need not be congruent.
It is highly recommended to understand and practice all the congruencies mentioned in the chapter along with attempting practice questions on the same. The NCERT exemplar Class 9 Maths solutions chapter 7 will help you understand the problems in a detailed manner.
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