1. Warm Up 1. 36m of a tree cracked as if hinged. The tip of the tree hit the ground 24m from the base. How many meters up from the base of the tree is the crack? Sketch a picture 2. Are the following triples, yes or no? A. 8,15,17B. 10, 20, 24 3. How high on a building will a 15-foot ladder touch if the foot of the ladder is 5 feet from the building? 4. Find the other leg: one leg is 5 cm and the hypotenuse is 13 cm. (Give exact answers)

2. Answers

3. Special Right Triangles There are two special right triangles! We will use the Pythagorean Theorem to discover the relationships between the sides of the two special triangles.

4. Isosceles Right Triangle – a right triangle with two equal sides Each isosceles triangle is half a square so they appear in math and engineering frequently. If two sides are equal then the base angles are _________ The base angles of a right-isosceles triangle are ________ congruent 45 o

5. Investigation 1) 5 3 7 11

6. Isosceles Right Triangle Conjecture or 45-45-90 Rule In an isosceles right triangle, if the legs have length s, then the hypotenuse has length _______

7. Lets try a few: Find the missing sides 1) 2) x x 16 52 yy 52= x

8. Investigation 5 10 30° 2 8

9. The other special triangle is a If you fold an equilateral triangle along one of its altitudes you get a 30-60-90 triangle. Therefore, a 30-60-90 triangle is one half an equilateral triangle so it appears in math and engineering frequently as well. 60 30 Side across from 30 o is the shortest side, AIMS reference calls this side ____ Side across from 60 o is the medium side Side across from 90 o is the hypotenuse

10. 30-60-90 Triangle Conjecture In a 30-60-90 triangle, (easy as 1, 2, 3) if the shorter side has length s, (think 1s) then the hypotenuse has length _____ and the longer leg has length ______ 30 60

11. x 4. 6. 30 x y 12 30 y 15 x 5. examples:

12. 10 x 45 60 x y 21 y x 7. 8. 9.