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High School Mathematics - 2
8.14 Pythagorean Theorem - Examples

Theorem: In a right angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides.
If the length of the hypotnuse is c and the lengths of other two sides are b and a then according to the pythogorean theorem:
c2 = a2 + b2


Converse: In a triangle if the square of one side is equal to the squares on the sums of the other two sides, then the angle opposite to the first side is a right angle.
To prove: AB2 + BC2 = AC2

Example: Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of the diagonals.


Directions: Solve the following problems. Also write at least 10 examples of your own.
Q 1: The sides of a triangle are 7cm, 24cm, 25cm, check if this is a right angled triangle.
yes
no

Q 2: A ladder is placed in such a way such that its distance from the wall to the foot of the ladder is 5 cm, its top reaches a height of 12m from the ground. Find the length of the ladder.
12m
15m
13m

Q 3: Which of these is a Pythagorean triplet?
8, 9, 13
13, 12, 5
15, 8, 5

Q 4: A ladder 20m long reaches height of 16m above the ground. Find the distance of the foot of the ladder from the wall.
12 m
14 m
13 m

Q 5: The sides of a triangle are 50cm, 80cm, 100cm, check if this is a right angled triangle.
yes
no

Q 6: A ladder 20 m long reaches a height of 16m above the ground. Find the distance from the foot of the ladder to the wall.
12 m
17 m
13 m

Q 7: A person goes 10 m due east and then 30m due north. Find his distance from the starting point.
12m
10m
15m

Q 8: The sides of a triangle are 3cm, 8cm, 6cm, check if this is a right angled triangle.
yes
no

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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