Class 9 Math Chapter 13 Question Answer
Handwritten and composed notes Class 9 Math Chapter 13 Question Answer Sides and Angles of a Triangle of Chapter No.13: Sides and Angles of a Triangle Notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Sides and Angles of a Triangle for the students of Mathematics Science group of the (9 class) Matriculation and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Important notes of Class 9 Math Chapter 13 Question Answer for Matriculation part-I students.
- Complete Multiple Choice Questions (MCQs) of Chapter No.13: Sides and Angles of a Triangle 9th class Mathematics Science group in English medium.
- Complete Chapter exercise wise solved questions of Chapter No.13: Sides and Angles of a Triangle 9th class Mathematics Science group in English medium.
- Complete Chapter review exercise questions of Chapter No.13: Sides and Angles of a Triangle 9th class Mathematics Science group in English medium.
- Important definitions Asking in board question papers of Chapter No.13: Sides and Angles of a Triangle 9th class Mathematics Science group in English medium.
- Prove that if two sides of a triangle are unequal in length, the longer
side has an angle of greater measure opposite to it.
- Prove that if two angles of a triangle are unequal in measure, the
side opposite to the greater angle is longer than the side opposite
to the smaller angle.
- Prove that the sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
- Prove that from a point, out-side a line, the perpendicular
is the shortest distance from the point on the line.
- Here are the detailed 9th class math chapter 13 question answer pdf to help you prepare for your exams.
- Introduction: Recall that if two sides of a triangle are equal, then the angles opposite to them are also equal and vice-versa. But in this unit we
shall study some interesting inequality relations among sides and
angles of a triangle.
- Theorem 13.1.1: If two sides of a triangle are unequal in length, the longer
side has an angle of greater measure opposite to it.
- Given: In ∆ABC, mAC > mAB
- To Prove: m ∠ ABC > m ∠ ACB
- Construction: On AC take a point D such that AD ≅ AB. Join B to D so that ∆ADB
is an isosceles triangle. Label ∠ 1 and ∠ 2 as showAn in the given figure.
- Example 1: Prove that in a scalene triangle, the angle opposite to the largest side is of measure greater than 60°. (i.e., two-third of a
right angle)
- Given: In ABC, mAC > mAB mAC, mAB > mBC, To Prove: m ∠ B > 60°.
- Example 1: Which of the following sets of lengths can be the lengths of
the sides of a triangle?
(a) 2 cm , 3 cm , 5 cm (b) 3 cm , 4 cm , 5 cm (c) 2 cm, 4cm , 7 cm
- (a) ∴ 2 +
3 = 5 . ∴ This set of lengths cannot be those of the sides of a triangle.
- (b) ∴ 3 + 4 > 5, 3 + 5 > 4, 4 + 5 > 3. ∴ This set can form a triangle.
- (c) ∴ 2 + 4 < 7
∴ This set of lengths cannot be the sides of a triangle.
- You can also download the 9th class math chapter 13 question answer pdf download for free.
- Example 2
Prove that the sum of the measures of two sides of a triangle
is greater than twice the measure of the median which bisects the
third side.
- 1. Two sides of a triangle measure 10 cm and 15 cm. Which of the
following measure is possible for the third side? (a) 5 cm (b) 20 cm (c) 25 cm (d) 30 cm
- 2. Prove that in a right-angled triangle, the hypotenuse is longer than each of the other two sides.