Transcript Slide 1

7.3 Special Right Triangles

Use properties of 45° - 45° - 90° triangles
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Use properties of 30° - 60° - 90° triangles
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Right triangles whose angle measures
are 45° - 45° - 90° or 30° - 60° - 90° are
called special right triangles. The
theorems that describe the relationships
between the side lengths of each of
these special right triangles are as
follows:
Theorem 7.6
In a 45°- 45°- 90°
triangle, the length of
the hypotenuse is √2
times the length of a
leg.
hypotenuse = √2 • leg
45 °
x√2
45 °
WALLPAPER TILING The wallpaper in the figure can
be divided into four equal square quadrants so that
each square contains 8 triangles. What is the area of
one of the squares if the hypotenuse of each
45°- 45°- 90° triangle measures
millimeters?
The length of the hypotenuse of one 45°- 45°- 90°
triangle is
millimeters. The length of the hypotenuse
is
times as long as a leg. So, the length of each leg is
7 millimeters.
The area of one of these triangles is
or 24.5 millimeters.
Answer: Since there are 8 of these triangles in one
square quadrant, the area of one of these
squares is 8(24.5) or 196 mm2.
WALLPAPER TILING If each 45°- 45°- 90° triangle in
the figure has a hypotenuse of
millimeters, what
is the perimeter of the entire square?
Answer: 80 mm
Find a.
The length of the hypotenuse of a 45°- 45°- 90° triangle
is
times as long as a leg of the triangle.
Divide each side by
Rationalize the denominator.
Multiply.
Divide.
Answer:
Find b.
Answer:
Be sure you realize the
Theorem 7.7
shorter leg is opposite the
 In a 30°- 60°- 90°
30° & the longer leg is
opposite the 60°.
triangle, the length
of the hypotenuse
60 °
is twice as long as
the shorter leg, and
the length of the
30 °
longer leg is √3
x√3
times as long as the
shorter leg.
Hypotenuse = 2 ∙ shorter leg
Longer leg = √3 ∙ shorter leg
Find QR.
is the longer leg,
hypotenuse.
is the shorter leg, and
is the
Multiply each side by 2.
Answer:
Find BC.
Answer: BC = 8 in.
COORDINATE GEOMETRY
is a 30°-60°-90°
triangle with right angle X and
as the longer leg.
Graph points X(-2, 7) and Y(-7, 7), and locate point W
in Quadrant III.
Graph X and Y.
lies on a horizontal gridline of the
coordinate plane. Since
will be perpendicular to
it lies on a vertical gridline. Find the length of
is the shorter leg.
is the longer
leg. So,
Use XY to find
WX.
Point W has the same x-coordinate as X. W is located
units below X.
Answer: The coordinates of W are
or about
COORDINATE GEOMETRY
is at 30°-60°-90°
triangle with right angle R and
as the longer leg.
Graph points T(3, 3) and R(3, 6) and locate point S in
Quadrant III.
Answer: The coordinates of S are
or about
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Pre-AP Geometry:
Pg. 360 #12 – 28, 36, 38
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Geometry:
Pg. 360 #12 – 24 and 36