Grade 8 Mathematics
In a RIGHT TRIANGLE, the square of the hypotenuse equals the sum of the squares of the two legs.
The formula is: a² + b² = c²
The HYPOTENUSE (c) is always the LONGEST side, opposite the right angle!
Key Terms:
Legs (a and b): The two shorter sides that FORM the right angle
Hypotenuse (c): The longest side, OPPOSITE the right angle
A right triangle has legs of 6 and 8. Find the hypotenuse.
Write the formula: a² + b² = c²
Substitute the leg values: 6² + 8² = c²
Square each term: 36 + 64 = c²
Add: 100 = c²
Take the square root: c = 10
A right triangle has one leg of 5 and a hypotenuse of 13. Find the other leg.
Write the formula: a² + b² = c²
Substitute (c is ALWAYS the hypotenuse!): a² + 5² = 13²
Square the known values: a² + 25 = 169
Subtract to isolate a²: a² = 169 - 25 = 144
Take the square root: a = 12
WRONG: If given hypotenuse = 10 and leg = 6, writing 10² + 6² = c². This makes the hypotenuse a leg!
RIGHT: The hypotenuse (10) is c, so write: a² + 6² = 10², then solve for a. Always identify which side is the hypotenuse FIRST!
Find the distance between points (1, 2) and (4, 6).
This creates a right triangle on the coordinate plane!
Find horizontal distance (a): 4 - 1 = 3
Find vertical distance (b): 6 - 2 = 4
Use Pythagorean Theorem: 3² + 4² = c²
Solve: 9 + 16 = 25, so c = 5
Distance = 5 units
3-4-5 | 5-12-13 | 8-15-17 | 7-24-25
And their multiples: 6-8-10, 9-12-15, 10-24-26, etc.
1. Find the hypotenuse: legs are 9 and 12
9² + 12² = c² → + = c² → c =
2. Find the missing leg: one leg is 8, hypotenuse is 17
a² + 8² = 17² → a² = - → a =
3. Find the distance between (2, 1) and (6, 4).
Horizontal: Vertical: Distance:
4. A ladder leans against a wall. The base is 6 feet from the wall. The ladder reaches 8 feet up the wall. How long is the ladder?
Ladder length = feet