Lesson 18 of 1524
Geometry
Angles in a triangle add to 180°, and a right triangle obeys a² + b² = c².
Practice this chapterPerimeter is the distance around. Area covers the surface. For a rectangle, perimeter is 2l + 2w and area is lw.
A circle with radius r has circumference 2πr and area πr². When a figure is scaled by k, lengths scale by k and areas scale by k².
Pythagorean theorem
a² + b² = c²
c is the side opposite the right angle, the longest side.
Worked example
A right triangle has legs 6 and 8. How long is the hypotenuse?
- 1The hypotenuse is the side opposite the right angle, and it is the longest side. The relation is a² + b² = c².
- 2Square the legs: 6² = 36 and 8² = 64.
- 3Add them: 36 + 64 = 100, so c² = 100.
- 4c = √100 = 10, because 10 × 10 = 100 and a length is positive.
- 5Check: 6² + 8² = 100 and 10² = 100. The two sides of the theorem match.
Result: 10
Why. The squares of the legs add to the square of the hypotenuse. 36 + 64 is 100, which is 10 squared, so the hypotenuse is 10. Adding the legs themselves, 6 + 8 = 14, is the wrong operation.
The interior angles of a triangle add to 180°, not 360°. A full turn is 360°.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.