1. Problem statement. I will explain what a 90 degree (right) triangle is and show a drawing. 2. Definition. A 90 degree triangle, also called a right triangle, has one angle equal to 90 degrees. The sides that form the right angle are called legs and the opposite side is the hypotenuse. 3. Key formula (Pythagorean theorem) and rules. For a right triangle with legs $a$ and $b$ and hypotenuse $c$, the Pythagorean theorem is: $$c^2 = a^2 + b^2$$ Important rules: legs are perpendicular; the hypotenuse is the longest side. 4. Example: compute hypotenuse when $a=3$, $b=4$. Use the formula above to compute $c$. $$c^2 = 3^2 + 4^2$$ $$c^2 = 9 + 16$$ $$c^2 = 25$$ $$c = \sqrt{25}$$ $$c = 5$$ 5. Area formula and demonstration with cancellation. Area formula is: $$A = \frac{1}{2}ab$$ Take $a=6$, $b=8$ as an example. $$A = \frac{1}{2}\cdot 6 \cdot 8$$ Show as a single fraction: $$A = \frac{1\cdot 6 \cdot 8}{2}$$ Cancel common factor 2 from numerator and denominator: $$A = 1\cdot 6 \cdot \frac{\cancel{8}}{\cancel{2}}$$ Now evaluate the canceled fraction $\frac{8}{2}=4$: $$A = 1\cdot 6 \cdot 4$$ $$A = 24$$ 6. Final answer and drawing instruction. A 90 degree triangle is a triangle with one 90 degree angle; examples above compute its hypotenuse and area. The drawing below shows a right triangle with vertices labeled A (right angle), B, and C.