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### High School Mathematics - 28.14 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: 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.13m12m15m Q 2: Two poles 6m and 11m stand on a plane ground. If the distance between their feet is 12m, determine the distance between their tops.13 m11 m12 m Q 3: The sides of a triangle are 7cm, 24cm, 25cm, check if this is a right angled triangle.noyes Q 4: Which of these is a Pythagorean triplet?15, 8, 58, 9, 1313, 12, 5 Q 5: 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.13 m12 m17 m Q 6: Triangle PQR is equilateral. QR = 30 units, B is the midpoint of QA. QA is perpendicular to PR. What is the length of PB? 19.84 cm24 cm23 cm Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!