Class 10 Maths Chapter 8 Notes

Important full class 10 maths chapter 8 notes Projection of a side of a triangle of Mathematics 10th class by Dear Respectable Sir M. Ramzan Suib. These handwritten and Composed notes are very helpful in the preparation of Problems of class 10 maths chapter 8 notes for students of the 10th class Mathematics and these are according to the paper patterns of all Punjab boards.

• Important class 10 maths notes chapter 8 for all students of Punjab  Textbook Board.
• Important MCQs of Chapter No.8: Projection of a side of a triangle of Mathematics 10th class.
• Important definitions of Chapter No.8: Projection of a side of a triangle of Mathematics 10th class.
• Solutions of Chapter No.8: Projection of a side of a triangle of Mathematics 10th class.
• Important problems of Chapter No.8: Projection of a side of a triangle of Mathematics 10th class.
• In this unit, students will learn how to:
• Prove the following theorems along with corollaries and apply them to solve appropriate problems.
• Important class 10th maths chapter 8 notes for all students of Punjab  Textbook Board.
• In an obtuse-angled triangle, the square on the side opposite to the obtuse angle is equal to the sum of the squares on the sides containing the obtuse angle together with twice the rectangle contained by one of the sides, and the projection on it of the other.
• In any triangle, the square on the side opposite to an acute angle is equal to the sum of the squares on the sides containing that acute angle diminished by twice the rectangle contained by one of those sides and the projection on it of the other.
• In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side (Apollonius' Theorem).
• The projection of a given point on a line segment is the foot of ⊥ drawn from the point on that line segment. If CD ⊥ AB, then evidently D is the foot of perpendicular CD from the point C on the line segment AB.
• The projection of a line segment CD on a line segment AB is the portion EF of the latter intercepted between foots of the perpendiculars drawn from C and D. However projection of a vertical line segment CD on a line segment AB is a point on AB which is of zero dimension.
• MISCELLANEOUS EXERCISE 8:
• 1. In a AABC, m ∠ A = 60° , prove that (BC)² = (AB)² + (AC)² - mAB . mAC.
• 2. In a AABC, m ∠ A = 45° , prove that (BC)² = (AB)² + (AC)² - √2 mAB . mAC.
• 3. In a ∆ABC, calculate mBC when mAB = 5 cm, mAC = 4 cm, m ∠ A = 60°.
• 4. In a ∆ABC, calculate mAC when mAB = 5 cm, mBC = 4√2 cm, m ∠ B = 45°.
• 5. In a triangle ABC, mBC = 21 cm, mAC = 17 cm, mAB = 10 cm. Measure the length of projection of AC upon BC.
• 6. In a triangle ABC, mBC = 21 cm. mAC = 17 cm, mAB = 10 cm. Calculate the projection of AB upon BC.
• 7. In a ∆ABC, a 17 cm, b = 15 cm and c = 8 cm. Find m ∠ A.
• 8. In a ∆ABC, a = 17 cm, b = 15 cm and c 8 cm find m ∠ B.
• 9. Whether the triangle with sides 5 cm, 7 cm, 8 cm is acute, obtuce or right angled.
• 10. Whether the triangle with sides 8 cm, 15 cm, 17 cm is acute, obtuce or right angled.
• In a parallelogram ABCD prove that (AC)² + (BC)² = 2 [ (AB)² + (BC)² ]