Download Lesson 11-5.notebook

Lesson 11­5.notebook
April 15, 2013
Review
Rule for Multiplying Square Roots
For nonnegative numbers (positive numbers) the square root a a
product equals the product of the square root.
Algebra
Arithmetic
If a ≥ 0 and b ≥ 0
then ab = √a * √b
√9*2 = √9 * √2
Apr 2­4:23 PM
What kind of triangle is this?
45°
90°
45°
In an isosceles right triangle the two acute angles are congruent. Since the sum of the measures of these two angles is 900, each angle measures 450. For this reason, an isosceles right triangle is often called a 450 right triangle.
Mar 30­3:22 PM
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Lesson 11­5.notebook
April 15, 2013
Using the Pythagorean Theorem what is the
length of the hypotenuse?
45°
√2
a2 + b2 = c2
1 unit
90°
45°
1 unit
12 + 12
1 + 1
2
√2
√2
= c2
= c2
= c2
= √c 2
=c
Replace a and b with 1
Simplify
Add
Find the square root
Leave as a radical
Mar 30­4:41 PM
Find the length of the hypotenuse using the
Pythagorean Theorem
45°
2√2
a2 + b2 = c2
2 units
90°
45°
2 units
45°
3√2
3 units
22 + 22 = c2
4 + 4 = c2
8 = c2 Find the square root
√8 = √c2
√4*2= c Use the rule for Multiplying Square Roots
2√2 = c Simplify
90°
45°
3 units
Apr 2­3:54 PM
2
Lesson 11­5.notebook
April 15, 2013
45°
s√2 units
s units
If each leg of a 45 0 right triangle is s units
long, then the hypotenuse is s√2 units long.
90°
45°
s units
Triangles
In a
triangle, the legs are congruent and the
length of the hypotenuse is the length of a leg times √2.
Hypotenuse = leg * √2 or s√2 with s being the side
length.
Mar 30­9:03 PM
Equilateral Triangle
B
What is the angle measurement of angle DBC and
DBA?
Pull
Pull
60°
Segment BD is a pepindicular bisector of
ABC creating two congruent right triangles.
300
11.4
11.4
Pull
Pull
What is the length of segment AD and segment DC?
5.7 units
60°
60°
A
D
C
11.4
Mar 30­8:26 PM
3
Lesson 11­5.notebook
April 15, 2013
Equilateral Triangle
B
Find the length of line segment BD.
60°
a2 + b2 = c2
2
12 + b 2 = 22
1 + b2 = 4
-1
-1
√b2=√3
2
2s
s√3
b = √3
b = √3
Erase to find the solution.
60°
60°
A
D
s
C
2
Mar 30­9:11 PM
30o-60o-90oTriangles
(
A
30ο
s√3 units
B
2s units
s units
If the shorter leg of a 300 - 600 -90o right
triangle is s units long, then the
longer leg is s√3 units long, and the
hypotenuse is 2s units long.
C
Triangles Rule
In a
triangle, the length of the hypotenuse is
2 times the length of the shorter leg. The length of the
longer leg (across from the 60oangle) is the length of the
shorter leg times √3.
Mar 30­9:31 PM
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Lesson 11­5.notebook
April 15, 2013
Mar 31­11:43 AM
Apr 15­12:26 PM
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Lesson 11­5.notebook
April 15, 2013
Apr 3­9:11 AM
Apr 3­9:12 AM
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Lesson 11­5.notebook
April 15, 2013
Apr 3­9:12 AM
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