21
CC Geometry R
Aim #22: What is the relationship in an isosceles right triangle?
Do Now: Find the measures of the missing sides in the given triangles.
10
14
600
300
450-450-900 Triangle
An isosceles right triangle has leg lengths of 1 as shown to the right.
a. The measures of the two acute angles are ____ and ____.
1
b. Use the Pythagorean Theorem to determine the length
of the hypotenuse.
1
c. Solve for the hypotenuse in the two isosceles right triangles below.
a)
b)
3
5
3
5
d. Conclusion: The ratio of the leg to the hypotenuse: _____ : _____
Practice: Solve for the missing sides in the following isosceles right triangles.
1)
2)
3)
8√ 2
6
4
4)
5)
6)
3√ 3
20
12
7)
8)
√5
9)
3
√6
10) The area of a square is 36 square inches. Find the exact value of the length
of the diagonal.
11) The altitude of an equilateral triangle measures
a) Find the perimeter of the triangle.
inches.
b) Find the exact area of the triangle.
12) The altitude of an equilateral triangle measures 12 inches.
a) Find the perimeter of the triangle.
b) Find the exact area of the triangle.
13) Find the exact length of a side of a square whose diagonal is:
a) 14 inches.
b) 20 inches
14) Use the diagram to find:
B
BC______ AD ______ CD ______ BD ______
50
450
C
300
D
A
15) Use the diagram below to find AB, BC and CD.
A
3√6
300
12
6√2
B
3√2
450
C
D
6√2
16) Find the values of x and y.
(Hint: Find the height of the triangle, first using the left triangle.)
8√2
4√2
4√6
17) Find the length of AB. (Hint: Find m≮ECD, first. Then, find CD. Then, find BC.)
E
8
A
4√3
4√3
2√3
300
B
6
10
C
4
D
18) ∆ABC is an equilateral triangle and ∆ADC is an isosceles triangle.
If AD = 12, find the area of the shaded region.
Area of ΔADC
1
A = (12 3)(6)
2
36√3
B
D
12
A
300
6√3
Area of ΔABC
1
A = (12 3)(18)
2
108√3
6
6√3
C
Shaded Area
108√3 - 36√3
72√3