January 13, 2017
January 13, 2017
2(3x + 8) = 46
6x + 12 = 46 '
6x = 34
6 6 _
x = 5.6
January 13, 2017
Aim #21: What is the relationship in an isosceles right triangle?
CC Geometry R
Do Now: Find the measures of the missing sides in the given triangles.
10
14
600
300
0
0
0
45 -45 -90 Triangle
An isosceles right triangle has leg lengths of 1 as shown to the right. 1
a. The measures of the two acute angles are ____ and ____.
1
b. Use the Pythagorean Theorem to determine the length
of the hypotenuse.
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
6)
5)
4)
3√ 3
20
12
9)
8)
7)
√6
√5
3
January 13, 2017
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
300
450
C
D
A
January 13, 2017
15) Use the diagram below to find AB, BC and CD.
A
300
12
B
450
D
C
16) Find the values of x and y.
(Hint: Find the height of the triangle, first using the left triangle.)
17) Find the length of AB. (Hint: Find m≮ECD, first. Then, find CD. Then, find BC.)
E
8
A
300
B
10
C
D
18) ∆ABC is an equilateral triangle and ∆ADC is an isosceles triangle.
If AD = 12, find the area of the shaded region.
B
D
A
300
C
January 13, 2017
Name_____________________________
CC Geometry R
Date __________________
HW #21
1) Find, in simplest radical form, the length of the hypotenuse of a right
triangle whose legs have length 20 and 10.
2) Find the length of the longer leg of a right triangle whose hypotenuse is 25
and shorter leg has length 15.
3) Cam sailed his boat due south for 38 miles, then due west for 25 miles. To the
nearest tenth of a mile, how far is Cam from where he began? (Hint: draw a right
triangle)
4) Is a triangle with sides of 10,
, and
a right triangle? Show work.
5) Find the lengths of the legs of the triangle.
100
450
6) Use the following diagram to find the lengths of:
B
AB_____ AC______ DC ______ DB______
10
300
450
C
D
A
January 13, 2017
7) Find the exact value of the length of the altitude of an equilateral triangle
whose side measures 12 inches.
8) The diagonal of a square measures
. Find the perimeter of the square.
0
9) In isosceles ΔABC, vertex angle C measures 120 and the length of AC is 8.
a) Find the length of the altitude to side AB.
b) Find the exact length of AB.
B
Review
Given: BD bisects ≮ABC
≮BAD ≅ ≮BCD
Prove: ≮DAC ≅ ≮DCA
D
A
_________Statements
C
Reasons___________________