NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4.
- Triangles Class 9 Ex 7.1
- Triangles Class 9 Ex 7.2
- Triangles Class 9 Ex 7.3
- Triangles Class 9 Ex 7.4
- Triangles Class 9 Ex 7.5
Board | CBSE |
Textbook | NCERT |
Class | Class 9 |
Subject | Maths |
Chapter | Chapter 7 |
Chapter Name | Triangles |
Exercise | Ex 7.4 |
Number of Questions Solved | 6 |
Category | NCERT Solutions |
NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4
Ex 7.4 Class 9 Maths Question 1.
Show that in a right angled triangle, the hypotenuse is the longest side.
Solution:
Ex 7.4 Class 9 Maths Question 2.
In given figure sides AB and AC of Δ ABC are extended to points P and Q respectively. Also, ∠PBC ∠QCB. Show that
AC > AB.
Solution:
Ex 7.4 Class 9 Maths Question 3.
In figure ∠B <∠A and ∠C<∠D.show that AD<BC
Solution:
Ex 7.4 Class 9 Maths Question 4.
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see fig.). Show that ∠A > ∠C and ∠B > ∠D.
Solution:
Given: ABCD is a quadrilateral. AB is the shortest side and CD is the longest side.
To Prove : ∠A> ∠C and ∠B > ∠D.
Construction: Join A and C, also B and D.
Proof: In Δ ABC, AB is the smallest side.
BC > AB
∠1 > ∠2 …(i)
[∵ angle opposite to longer side greater]
Ex 7.4 Class 9 Maths Question 5.
In the figure, PR > PQ and PS bisect ∠QPR. Prove that ∠PSR > ∠PSQ.
Solution:
In Δ PQR, we have
Ex 7.4 Class 9 Maths Question 6.
Show that of all line segments drawn from a given point, not on it, the perpendicular line segment is the shortest.
Solution:
Given: x is a line and A is a point not lying on x. AB ⊥ x, C is any point on x other than B.
To prove : AB < AC
Proof: In ΔABC, ∠B is the right angle.
∴ ∠C is an acute angle.
∴ ∠B > ∠C
=> AC >AB
(∵ the Side opposite to greater angle is longer)
=>AB< AC
Hence, the perpendicular line segment is the shortest.
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