Class 9 Math Chapter 15 Question Answer
Handwritten and composed notes Class 9 Math Chapter 15 Question Answer Pythagoras’ Theorem of Chapter No.15: Pythagoras Theorem notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Pythagoras’ Theorem 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 15 Question Answer for Matriculation part-I students.
- Complete Multiple Choice Questions (MCQs) of Chapter No.15: Pythagoras’ Theorem 9th class Mathematics Science group in English medium.
- Complete Chapter exercise solved questions of Chapter No.15: Pythagoras’ Theorem 9th class Mathematics Science group in English medium.
- Complete Chapter review exercise questions of Chapter No.15: Pythagoras’ Theorem 9th class Mathematics Science group in English medium.
- Important definitions Asking in board question papers of Chapter No.15: Pythagoras’ Theorem 9th class Mathematics Science group in English medium.
- Prove that in a right-angled triangle, the square of the length of
hypotenuse is equal to the sum of the squares of the lengths of the
other two sides. (Pythagoras’ theorem).
- Prove that if the square of one side of a triangle is equal to the sum
of the squares of the other two sides, then the triangle is a right
angled triangle (converse to Pythagoras’ theorem).
- Here are the detailed 9th class math chapter 15 question answer pdf to help you prepare for your exams.
- Introduction: Pythagoras, a Greek philosopher and mathematician discovered the simple but important relationship between the sides
of a right-angled triangle. He formulated this relationship in the form
of a theorem called Pythagoras’ Theorem after his name. There are
various methods of proving this theorem. We shall prove it by using
similar triangles. We shall state and prove its converse also and then
apply them to solve different problems.
- Pythagoras Theorem 15.1.1: In a right angled triangle, the square of the length of hypotenuse is equal to the sum of the squares of the lengths of
the other two sides.
- Given: ∆ACB is a right angled triangle in which mC = 90° and mBC = a, mAC = b and mAB = c.
- To Prove: c^2= a^2
+ b^2
- Construction: Draw CD perpendicular from C on AB. Let mCD = h, mAD = x and mBD = y. Line segment CD splits ∆ABC into two ∆s ADC and BDC which are separately shown in the figures
(ii) -a and (ii) -b respectively.
- Corollary: In a right angled ∆ABC, right angle at A,
- Remark: Pythagoras’ Theorem has many proofs. The one we have given
is based on the proportionality of the sides of two similar triangles.
For convenience ∆s ADC and CDB have been shown separately.
Otherwise, the theorem is usually proved using figure (i) only.
- You can also download the 9th class math chapter 15 question answer pdf download for free.
- Theorem 15.1.2 [Converse of Pythagoras’ Theorem 15.1.1]: If the square of one side of a triangle is equal to the sum
of the squares of the other two sides, then the triangle is a right
angled triangle.
- A student travels to his school by the route as shown in the figure. Find mAD direct distance from his house to school.
- In this unit we learned to state and prove Pythagoras’ Theorem and
its converse with corollaries.
- In a right angled triangle, the square of the length of hypotenuse
is equal to the sum of the squares of the lengths of the other two
sides.
- If the square of one side of a triangle is equal to the sum of the
squares of the other two sides then the triangle is a right angled
triangle.
- Moreover, these theorems were applied to solve some questions of practical use.