1. Unit 7A - Lesson #6: Special Right Triangles (Textbook Section 7-3)
Grab a Lesson #6 example sheet and complete the Warm-Up box on the front.

2. Warm-Up:
(1) (2) 5 w
45 6 y
= w2
= y2
50 = w2
72 = y2

3. Warm-Up:
45 z
(3) (4) 8 x

4. Isosceles Right Triangles
Warm-Up:
(1) What type of triangles are we dealing with in each figure above?
(2) In regards to the lengths of the sides of each triangle, what pattern can you observe in each triangle? Describe the pattern below.
Isosceles Right Triangles
Legs are always the same length.
Hypotenuse Length = Leg x

5. Isosceles Right Triangles (45- 45- 90)x
Any right triangle with congruent leg lengths.
Mathematical Relationship:
Leg 1 = Leg 2 = __________
Hypotenuse = ___________ x

6. Examples of the (45- 45- 90)
Finding the Hypotenuse
45 9 k
k = =

7. Examples of the (45- 45- 90)
Finding a Leg
g = =
45 g =

8. Example #1: Missing Sides of Isosc. Tri.7
(A) x = _________ (B) x = _________
y = ________ y = ________
45 7 y x
45 x y

9. Example #1: Missing Sides of Isosc. Tri.9
(C) x = _________ (D) x = _________ x x 13

10. x 2x 2x x 30- 60- 90 Triangles Mathematical Relationship:
Leg opposite 30 = ________
Leg opposite 60 = ________
Hypotenuse = ________
30 x 2x
60 x 2x
KEY Side!!!!!

11. Examples of the 30- 60- 90
30 5 h
60 s
h =
= 10
s = =

12. Examples of the 30- 60- 90
30 h
60 s
h = =
s =
s =
s =

13. Examples of the 30- 60- 90
s =
30 h
h = =
60 s

14. Example #2: Missing Sides of 30-60-90 Tri.24 15
(A) x = _________ (B) x = _________
y = ________ y = ________ y x
30 x y

15. Example #2: Missing Sides of 30-60-90 Tri.
(C) x = _________ (D) x = _________
y = ________ y = ________
60 x y
30
60 18 x y

16. Example #3: Right Triangles in Other Shapes5
(A) Perimeter = _________
Hint: Where could we “create” a right triangle?
45 7 7
45 5 7

17. What are the angle measures in an equilateral triangle???
Example #3B:
The yield sign at right is an equilateral triangle with sides of length 24 inches. Determine the height of the sign. 12 12
What are the angle measures in an equilateral triangle???
60
60 h 24
30 12
60
30
Find the long leg…
h =
The height of the sign is ≈ 20.8 inches

18. Homework Time!!!!