Grade 7 Pythagoras' Theorem

Concept: A right-angled triangle is a triangle that has one angle exactly equal to 90 degrees.

Hypotenuse: The side opposite the right angle. It is always the longest side of a right-angled triangle.

Legs (or Sides): The two sides that form the right angle.

Diagram:

Theorem: In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (the legs).

Formula: If 'c' is the length of the hypotenuse and 'a' and 'b' are the lengths of the legs, the theorem can be written as:

c² = a² + b²

Explanation: This means if you draw squares on each side of a right-angled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the two legs.

Step 1: Identify the given values. The lengths of the legs are a = 3 cm and b = 4 cm. We need to find the hypotenuse, c.

Step 2: Use Pythagoras' Theorem:

c² = a² + b²

Step 3: Substitute the values into the formula:

c² = 3² + 4²

Step 4: Calculate the squares and add them.

3² = 3 * 3 = 9

4² = 4 * 4 = 16

c² = 9 + 16

c² = 25

Step 5: Find the square root of the result to get the length of the hypotenuse.

c = square root of 25

c = 5

Result: The length of the hypotenuse is 5 cm.

Step 1: Identify the given values. The hypotenuse is c = 13 cm, and one leg is a = 5 cm. We need to find the other leg, b.

Step 2: Use Pythagoras' Theorem:

c² = a² + b²

Step 3: Substitute the values into the formula:

13² = 5² + b²

Step 4: Calculate the squares.

13² = 13 * 13 = 169

5² = 5 * 5 = 25

169 = 25 + b²

Step 5: Isolate b² by subtracting 25 from both sides.

169 - 25 = b²

144 = b²

Step 6: Find the square root of the result to get the length of the leg.

b = square root of 144

b = 12

Result: The length of the other leg is 12 cm.