33
Properties of Right Triangles
Properties of
Right
Triangles
Table of Contents
DAY 1: (Ch. 5-7) SWBAT: Solve Problems Using the Pythagorean’s Theorem and its Converse Pgs: 1-5 HW: Pg: 6
DAY 2: (Ch. 5-8) SWBAT: Solve Problems involving 45-45-90 Special Right Triangles
Pgs: 7-13
HW: Pgs: 14-15
DAY 3: (5-8) SWBAT: Solve Problems involving 30-60-90 Special Right Triangles
Pgs: 16-22
HW: Pgs: 23-25
DAY 4: (Review) SWBAT: Solve Problems involving Right Triangles
Pgs: 26-31
DAY 5: QUEST
1
Day 1 - PYTHAGOREAN’S THEOREM
The Pythagorean Theorem is probably the most famous mathematical relationship. As you learned in recent
years, it states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the
length of the hypotenuse.
Warm – Up
2
3
The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know
the side lengths.
4
Summary
CONVERSE of the Pythagorean’s Theorem
5
Challenge
Exit Ticket
6
Day 1 - HW
2 10 5
5
1
7
Day 2 – Special Right Triangles (45-45-90)
Warm - Up
Use the information marked on the figure to find the value of x. Express all answers in simplest radical form.
1.
2.
X
√5
2
8
Example 1: Find the length of the diagonal.
a) b) c)
8
8 x x
25
25
6 2
6 2
x
9
1) 2) 3)
d. fdf e. f.
10
10 x x
17
17
8 2
8 2
x
10
fdf
4. 5.
Example 2: Find the length of each side.
g) h) i)
x
x 2 2
x
x 40 2
x
x 6
11
6) 7) 8)
j. k. l.
x
x 2
x
x 13 2
x
x 4
12
jkjk 9. 10. 11. Word Problems 12.
24 6
𝑦
13
13. SUMMARY: Rule for 45-45-90 Right Triangles Challenge
Exit Ticket
14
Day 2 - Homework
15
9)
10)
11)
12)
The perimeter of a square is 48 inches. What is the length of the diagonal?
16
Day 3 – Special Right Triangles (30-60-90)
Warm - up
Use the information marked on the figure to find the value of x. Express all answers in simplest radical form.
1. The perimeter of a square is 24 cm. Find the length of the diagonal of the square.
17
Example 1: Find the value of x and y.
a) b) c)
2 2
2
6 6
6
4 3
18
a) b) c)
5 5
5
14 14
14
9 3
19
20
21
Regents Questions
A.
B.
22
SUMMARY: Rule for 30-60-90 Right Triangles
Challenge
Exit Ticket
23
Day 3 – Homework
Use the information marked on the figure to find the value of x and y.
1.
2. 3.
4.
5. 6.
24
7.
8. 9.
10.
11.
12.
25
13. 14. 15. 16. 17.
26
Day 4 – Review
Pythagorean’s Theorem Review
1.
2.
27
3.
4.
5.
6. 6.
28
45-45-90 Special Right Triangles
7.
8. 9.
10. 11.
12. The perimeter of a square is 400 m. Calculate the length of the diagonal of the square.
13. The perimeter of a square is 36 m. Calculate the length of the diagonal of the square.
29
30-60-90 Special Right Triangles
14.
Use the information marked on the figure to find the values of the variables below.
15. 16.
17. 18.
19. 20.
18 15
11 3
9
30
21.
22.
23. The perimeter of an equilateral triangle measures 18 cm.
What is the length of the altitude?
24. The perimeter of an equilateral triangle measures 30 cm.
What is the length of the altitude?
31
Special Right Triangles Combo
25.
26.
27.
