1. 7.4 Special Right Triangles
OBJECTIVE:
To use relationships among the sides in special right triangles
on a piece of paper
draw 3 squares with
sides of 10, 8, and 2
(cm)
This should take 3-4 minutes max!

2. Quiz

3. now draw the other diagonals
Draw the diagonal on the 10 cm square.
Describe the angle measures of the square.
Explain what the diagonal represents.
What transformation happens by ‘folding’ along the diagonal?
What is the line of symmetry doing through the 90° angles?
What are the angles in one of those triangles?
If the diagonal is a line of symmetry (line of reflection), are the 2 resulting right triangles congruent?.
What other type of triangle is being formed besides a right triangle?)
each is 90°
it is a line of symmetry
A reflection
cutting them in half – it is an angle bisector.
Yes, because the triangle has been reflected over the line of symmetry.
Isosceles triangle
now draw the other diagonals

4. Is there a pattern, you suspect . . .
- Measure one side of each of your triangles, - then calculate the hypotenuse using Pythagorean theorem – simplify your answers, - then check it by measuring the diagonals 10 8 2
Is there a pattern, you suspect . . .

5. Ws homework
8 (triple)
4.94
Acute
Not a tiangle 14
29.84 feet

6. Homework P. 444 13. right triangle 23. triangle, obtuse 27. right
9. ~9.14 in.
sq. cm
28. 6
29.
31. about 127 feet
34. a)about 197 feet
B) about 19 trees
C) about $228
P. 444
13. right triangle
23. triangle, obtuse
27. right
< x < 16

7. ISOSCELES RIGHT TRIANGLES
notes
** **
ISOSCELES RIGHT TRIANGLES
leg
= hypotenuse

8. Solving Special Right Triangles using the ratios for the sides1 y 20 x
Find x and y.
X = 20

9. Set up proportion to solve special right triangles1 1 7 y y x x
Find x and y.
Find x and y.
X = 7

10. Set up proportion to solve special right triangles1 1 18 y y x x
Find x and y.
Find x and y.
X = 29

11. Solving
x2 = 8
x = 42 8 X

12. “Look OUT for” squares cut by a diagonalm h 18 12 k
square r 36
(A Triangle)

13. Elaborate:
1. The perimeter of a square is ft. Find the length of the diagonal of the square as well as the length of each side of the square.
2. Given the square shown below, find the perimeter and area.
36 cm

14. In class practice work 1-5, 12,13, 14
A leg of a triangle is 3in. Find the length of the hypotenuse.
2. Calculate the approximate length of a diagonal of a square with sides of 8
cm.
3. In ΔABC, <A is a right angle and m<B = 45° If AB = 30 feet, find AC.

15. . . . on the back of original paper
Use a ruler to draw a line segment of 12 cm length near the bottom edge of you piece of paper.
Use a protractor to measure a 60 ° angle at one end.
Measure from the vertex of the angle (that's the pointy bit) along the new line until it’s length matches the line segment from part one. Mark this spot.
Connect this point to the unattached end of the first line segment. You should now have an equilateral triangle.
Step 1
Step 2
Step 3

16. Construct the perpendicular bisector of the triangle
5. Arrange the sides of ∆ABD from smallest to largest.
1. Classify the triangle by it’s sides and by it’s angles. B
6. What is the length of AB? AD?
2. What are the angle measures of each of the triangle’s angles.
7. What is the length of BD? How can we verify?
3. What does the altitude of this triangle do to the triangle and it’s angles? A C
4. What other special segments are BD?. D
8. Using Pythagorean Thm find the simplified length of BD . . .

17. 30°-60°-90° Triangles
In a 30°-60°-90° Triangles, the hypotenuse is twice the length of the short leg and the long leg is times as long as the short leg. 60 2x 4 2 x 30

18. ** **
short leg *
= long leg
short leg * 2 = hypotenuse

19. Solving Special Right Triangles using the ratios for the sides
30°
60° 1 2 2 1 30 60 b 2
a² + b² = c²
1² + b² = 2²
b² = 4-1
b² = 3
b =

20. Set up proportion to solve special right triangles
30°
60° 1 2
30°
60° 1 2 12 y x y x 10
Find x and y.
Find x and y.
2x = 12(1)
X =6
X = 20

21. Set up proportion to solve special right triangles
30°
60° 1 2
30°
60° 1 2 y y x x
Find x and y.
Find x and y.

22. Set up proportion to solve special right triangles
30°
60° 1 2 y x
Find x and y.

23. Elaborate:
1. The perimeter of an equilateral triangle is 96 ft. Find the length of each side of the triangle as well as the altitude.
2. Given the rectangle shown below, find the diagonal length, vertical side length, perimeter and area.
60 24
Perimeter =
Area =

24. Ones to look for: 40 n m
Equilateral triangle
(A Triangle)

25. In class practice
6. The length of the hypotenuse of a triangle is m. Find the length of the side opposite the 30° angle.
7. The shorter leg of a triangle is 3.4 feet long. Find the perimeter.
8. The long leg of a is 27m. Find the length of the short leg and the hypotenuse.
9. In ΔABC, <A is a right angle and m<B = 30. If AB = 18 feet, find BC.
10. One angle of a right triangle is 60°. The side opposite this angle is 7. Find the length of the two remaining sides.

26. Classwork, finish
Practice
Ws 7.4 special right triangles

27. classwork 5 m 10.2 + 3.4 feet 9 + 18 12 3 , 6 Alt.=12; per = 24 6.2733 12
3 , 6
Alt.=12; per = 24
6.2733
1.2
= 40.5cm
9 in.
23.1 ft
3 ~5.196 cm
~10.39
43.5 feet
x=1.5, y=
Homework:
WS 7.4 special right triangles

28. WS 7.4 Special Rights a=22 + 4 b=8 m=2.25 x=2 ; y=2 x = 4; y =
wire = ; ht = 12
F; every to some T
F; either to shorter
F 60° to 30° 24 42
30° 9 36

29. classwork 1.2 km 4.999 feet (or 5’) 8.395 ~11.872 in. 127.3 feet
meters 8
3 in.
16 cm
30 feet 8
10 or both 5 7 14
.707 inch or
~7.483 feet
Book work:
Pg. 461: 3, 11, 17, 33
Pg. 909: 28, 30, 32

30. Book work Pg. 461: 7 11. t=4 ; u = 7 33. 45-45-90 for all trianglesc 10
Pg. 461:
t=4 ; u = for all triangles
b C. 1.5 in x 1.5 in.
Pg. 909:
28. x=7; y= a = b= 9
32. s = t =