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

Question 1.

Show that in a right angled triangle, the hypotenuse is the longest side.

Solution:

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:

Question 3.

In figure ∠B <∠A and ∠C<∠D.show that AD<BC

Solution:

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]

Question 5.

In the figure, PR > PQ and PS bisect ∠QPR. Prove that ∠PSR > ∠PSQ.

Solution:

In Δ PQR, we have

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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