Form 2 Mathematics – PYTHAGORAS THEOREM

PYTHAGORAS THEOREM

PYTHAGORAS THEOREM
Pythagoras theorem is used to solve problems involving right angled triangles.

Statement:

In a right- angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Shown below

Required to prove: c² = a² + b²

Construction : Joining L and N. Considering the trapezium PQLN:

Area of the trapezium

but area of trapezium = area Δ PKN + area Δ KQL + area Δ KLN

(a+b) (a+b) = ab + ( c x c)

(a+b) (a+b) = ab + c²

[a² + 2ab + b²] = ab + c²

a² + ab + b² = ab + c²

a² + b² = c²

Pythagoras theorem

Examples

1.The side s of a triangle containing the right angle have length of 5cm and 12cm.

Find the length of the hypotenuse

Solution

C²= a² +b²

C² = 5² + 12²

C² = 25+ 144

C² = 169

C =

C= 13cm

∴The length of the hypotenuse = 13cm.

2. In figure below if AC =17cm, BC = 8cm, and CD = 12cm find AD

Solution:

EXERCISE

1. Calculate the unknown side of the following triangle

SOLUTION:
17² = 15² + b²

b² = 17² – 15²

b² = 289 – 225

b =

b = 8cm

∴ r² = 8²+ 8²
r² = 64 +64

∴r =11.31cm

2. Given triangle ABC, where B = 90⁰.Find the lengths of the sides which are not given

3. A man travels 15km due north and then 8km due west. How far is he from his starting point?

Solution:

X² = 15² +8²

X² = 225 +64

X =

X = 17km

∴ He is 17km from his starting point

Find the area of the triangle and the length of the perpendicular from C to B.

Solution:

ALL NOTES FOR ALL SUBJECTS QUICK LINKS:

AGRICULTURE O LEVEL

PURE MATHEMATICS A LEVEL

BAM NOTES A LEVEL

BASIC MATH O LEVEL

BIOLOGY O/A LEVEL

BOOK KEEPING O LEVEL

CHEMISTRY O/A LEVEL

CIVICS O LEVEL

COMPUTER(ICT) O/A LEVEL

ECONOMICS A LEVEL

ENGLISH O/A LEVEL

COMMERCE O/A LEVEL

ACCOUNTING A LEVEL

GENERAL STUDIES NOTES

GEOGRAPGY O/A LEVEL

HISTORY O/A LEVEL

KISWAHILI O/A LEVEL

PHYSICS O/A LEVEL

MOCK EXAMINATION PAPERS

NECTA PAST PAPERS

Basic Mathematics Study Notes Form 2 Basic Mathematics Study Notes Msomi Maktaba All Notes FORM 2MATHEMATICS