Transcript Lesson 7.3 Two Special Right Triangles

Lesson 7.3 Two Special
Right Triangles
Objectives:
To use properties of 45-45-90 triangles
To use properties of 30-60-90 triangles
Mrs. McConaughy
Geometry
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Isosceles Right Triangle
Theorem
ISOSCELES
RIGHT
TRIANGLE
NOTE:
If you
are given the length of
THEOREM:theInhypotenuse,
an isosceles
you right
can determine the
triangle, if the legs have length, l,
length of a side by dividing
l it√2
then the hypotenuse
has length ____.
√2, then rationalizing the
by_________________________
denominator, when necessary.
___________________________.
Mrs. McConaughy
Geometry
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EXAMPLES:
Find the length of the hypotenuse in each isosceles triangle
below.
3√2
6√2
Mrs. McConaughy
4√2
5√2
7√2
12√2
Geometry
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Recall: Triangle Inequalities
If two angles of a triangle are not
congruent, then the longest side
largest angle
lies opposite the _______
and the shortest side lies opposite
smallest
the ________
angle.
Mrs. McConaughy
Geometry
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30-60-90 TRIANGLE THEOREM
30-60-90 TRIANGLE THEOREM: In a 30-6090 triangle, if the side opposite the 30 degree
angle has length, l, the hypotenuse has length
2l
_______.
NOTE: These triangles are sometimes referred
to as 1-2-√3 right triangles.
Mrs. McConaughy
Geometry
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Easy way to remember the
relationship among angles and sides in
30-60-90 triangles:
1. Rank order the following
numbers from smallest to
largest:
1, 2, √3
2l
60
1, √3 , 2
2. Now, use the Triangle
Inequality Theorem to
place the side
lengths 1l, √3l , 2l
opposite the
appropriate angles in a
30-60-90 triangle.
Mrs. McConaughy
30
l√3
NOTE: It is usually easier to
determine the length of the
shortest and longest sides,
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initially.
1l
Find the length of each indicated
side:
60
____
____
____
30
NOTE:
The
length
of
one
side
will
be
provided
Mrs. McConaughy
Geometry
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by your instructor.
Find the length of each indicated side.
Mrs. McConaughy
Geometry
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In summary:
We can find the lengths of sides in right
triangles by using:
30-60-90 ∆
Pythagorean Primitives
c
a
…and
∆
3 45-45-90
•4•5
5 • 12 • 13
l
their
! 2l
8 • 15 multiples
• 17
7 • 24 • 25 45
b
l
l√2
45
Pythagorean Theorem
c = a2 + b 2
Mrs. McConaughy
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Geometry
30
l√3
60
l
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Putting it all together:
Find the length of each indicated side.
20√3
8 ∙ 3
8 ∙5
__ =40
__
20
8 ∙ 4
Mrs. McConaughy
Geometry
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Homework Assignment:
Special Right Triangles WS (1-10 all, 12)
Mrs. McConaughy
Geometry
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