1. Triangle Review A scalene triangle has no sides and no angles equal. An isosceles triangle has two sides and two angles equal. An equilateral triangle has three sides and three angles equal.

2. A right triangle has one right angle. Identify the triangle below; right isosceles How are the three sides of a right triangle related to each other?

3. The Pythagorean Theorem a b c a 2 + b 2 = c 2 Hypotenuse, the longest side of a right triangle

4. 8 6 c Example 1: Calculate side c. c 2 = 8 2 + 6 2 c 2 = 64 + 36 c 2 = 100 c = 10 c 2 = a 2 + b 2

5. x 2 + 49 = 144 x 2 = 95 x = 9.7 Example 2: Calculate side x. 12 7 x a 2 + b 2 = c 2 x 2 + 7 2 = 12 2 x 2 = 144 – 49 hypotenuse

6. Similar Triangles Two triangles are considered to be similar if and only if: they have the same shape corresponding angles are equal the ratio of the corresponding side lengths are equal

7. Step 1: Identify two similar triangles. AB C DE F 72 cm 1 m 18.5 m x Δ ABC ~ Δ DEF Step 2: Write equivalent ratios Ex 1. Find x.

8. 72 cm 1 m 18.5 m xAB C DE F Step 4: Use the ratios that apply to solve for x. 0.72x = 18.5 x = 25.7 m

9. Ex #2: Surveyors have laid out triangles to find the length of a lake. Calculate this length, AB. Step 1: Draw a labeled diagram. Step 2: Identify two similar triangles. Δ ACB ~ Δ ECD Step 3: Write equivalent ratios PROVIDED ft

10. Step 4: Use the ratios that apply to solve for x. ft