Special Right Triangles Properties of 45°-45°-90° Triangles ____________ PERIOD _____ The sides of a 45°-45°-90° right triangle have a special relationship Example 1 If the leg of a 45°-45°-90° right triangle is x units show that the hypotenuse is x 2 units 45 x 2 Example 2 In a 45°-45°-90° right triangle the hypotenuse is 2 times the leg
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Study Guide and Intervention Special Right Triangles Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a special relationship
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Name Lou 8-3 Study Guide and Intervention Special Right Triangles Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a
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Study Guide and Intervention Special Right Triangles Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a e a special
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8-3 Study Guide and Intervention Special Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a special relationship If the leg of
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8-3 Study Guide and Intervention Special Right Triangles Properties of 45°-45°-90° Triangles The sides of a 45°-45°-90° right triangle have a special relationship Example 1 If the leg of a 45°-45°-90° right triangle is x units show that the hypotenuse is x ? 2 units 45 ° x ?? ° 45 Using the Pythagorean Theorem with b x then = = c2 a2 b2 = +
8-3 Study Guide and Intervention - The Masters Program
Special Right Triangles Properties of 30°-60°-90° Triangles The sides of a 30° -60° 90° right triangle also have a special relationship Example 1: In a 30°-60° 90° right triangle the hypotenuse is twice the shorter leg Show that the longer leg is ? times the shorter leg MNQ is a 30°-60°-90° right triangle and the length of the
NAME DATE PERIOD 8-3 Study Guide and Intervention
Special Right Triangles Properties of 45°-45°-90° Triangles ____________ PERIOD _____ The sides of a 45°-45°-90° right triangle have a special relationship Example 1 If the leg of a 45°-45°-90° right triangle is x units show that the hypotenuse is x 2 units 45 x 2 Example 2 In a 45°-45°-90° right triangle the hypotenuse is 2 times the leg
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NAME 8-2 Study Guide and Intervention (continued) The Pythagorean Theorem and Its Converse Converse of the Pythagorean Theorem If the sum of the squares of the lengths ofthe two shorter sides of a triangle equals the square of the lengths of the longest side then the PERIOD triangle is a right ffiangle
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Lesson 8-3 Study Guide and Intervention 429–430 one vertex of an n-gon separates the polygon into n 2 triangles The sum of the measures
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Chapter 8 20 Glencoe Geometry 8-3 Skills Practice Special Right Triangles Find x 1 45° 25 x 2 45° x 17 3 45° 48 x 4 45° 100 x 5 45° 100 x 6 45° 88 x 7 Determine the length of the leg of 45°-45°-90° triangle with a hypotenuse length of 26 8 Find the length of the hypotenuse of a 45°-45°-90° triangle with a leg length of 50
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8-3 Study Guide and Intervention 450 Special Right Triangles Exercises Find x 450 450 18 450 16 450 I a 450-450-900 triangle has a hypotenuse length of 12 find the leg length NJî 450 8 Determine the length of the leg of 450-450-900 triangle with a hypotenuse length of 25 inches Ire 9
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Example 2Example 1
Chapter 821Glencoe Geometry
Lesson 8-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-3Study Guide and Intervention
Special Right Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____Lesson 8-3Properties of 45°-45°-90° TrianglesThe sides of a 45°-45°-90° right triangle have a
special relationship.If the leg of a 45°-45°-90°
right triangle is xunits, show that the hypotenuse is x ?2?units.Using the Pythagorean Theorem with
a?b?x, then c 2 ?a 2 ?b 2 ?x 2 ?x 2?2x 2 c??2x 2 ?x?2? x?? xx 245?45?
In a 45°-45°-90° right
triangle the hypotenuse is ?2?times the leg. If the hypotenuse is 6 units, find the length of each leg.The hypotenuse is ?2?times the leg, so
divide the length of the hypotenuse by ?2?. a? ?3 ?2?units 6?2? 26?2? ?2??2? 6 ?2 ?Find x.
1. 2. 3.
4. 5. 6.
7.Find the perimeter of a square with diagonal 12 centimeters.
8.Find the diagonal of a square with perimeter 20 inches.
9.Find the diagonal of a square with perimeter 28 meters.
x 3??2 x18 xx 18 x 10x 45?3??2 x 845?
45?
Exercises
Example 1
Example 2
Chapter 822Glencoe Geometry
0-30-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-3Study Guide and Intervention (continued)
Special Right Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____ Properties of 30°-60°-90° TrianglesThe sides of a 30°-60°-90° right triangle also have a special relationship. In a 30°-60°-90° right triangle, show that the hypotenuse is twice the shorter leg and the longer leg is ?3?times the shorter leg. ?MNQis a 30°-60°-90° right triangle, and the length of the hypotenuse M ?N?is two times the length of the shorter side N?Q?.Using the Pythagorean Theorem,
a 2 ?(2x) 2 ?x 2 ?4x 2 ?x 2 ?3x 2 a??3x 2 ?x?3? In a 30°-60°-90° right triangle, the hypotenuse is 5 centimeters. Find the lengths of the other two sides of the triangle. If the hypotenuse of a 30°-60°-90° right triangle is 5 centimeters, then the length of the shorter leg is half of 5 or 2.5 centimeters. The length of the longer leg is ?3?times the length of the shorter leg, or (2.5) (?3?)centimeters.Find xand y.
1. 2. 3.
4. 5. 6.
7.The perimeter of an equilateral triangle is 32 centimeters. Find the length of an altitude
of the triangle to the nearest tenth of a centimeter.8.An altitude of an equilateral triangle is 8.3 meters. Find the perimeter of the triangle to
the nearest tenth of a meter. xy 60?20 xy 60?
12 xy 30?
9 ??3 x y 11 30?
xy 60?
8 x y
30?60?
1 2 xa NQP M 2x30?30?
60?60?
Exercises
Chapter 823Glencoe Geometry
Lesson 8-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.8-3Skills Practice
Special Right Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____Lesson 8-3
Find the exact values of xand y.
1. 2. 3.
4. 5. 6.
For Exercises 7-9, use the figure at the right.
7.If a?11, find band c.
8.If b?15, find aand c.
9.If c?9, find aand b.
For Exercises 10 and 11, use the figure at the right.10.The perimeter of the square is 30 inches. Find the length of B
?C?.11.Find the length of the diagonal B
?D?.12.The perimeter of the equilateral triangle is 60 meters. Find the
length of an altitude.13.?GECis a 30°-60°-90° triangle with right angle at E, and E
?C?is the longer leg. Find the coordinates of Gin Quadrant I for E(1, 1) and C(4, 1). E F GD 60?AB CD 45?
b AB C ac 60?
30?
y x
13131313
y x 60?16yx 45?8
yx 45?12
yx 30?32
yx 60?24
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Kuta Software - Infinite Geometry Name___________________________________Period____Date________________
Special Right Triangles
Find the missing side lengths. Leave your answers as radicals in simplest form. 1) a 22b
45°
2) 4 x y45°
3) x y 322
45°
4) x y 3245°
5) 6 x y45°
6) 26x y
45°
7) 16 x y60°
8) u v 230°
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9) u v 860°
10) 85x y
60°
11) x 53y
60°
12) 10 x y60°
13) 82u v
45°
14) x 12 y30°
15) 3 a b60°
16) a 11 3 b30°
17) 22a b
60°
18) 7 m n45°
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Kuta Software - Infinite Geometry Name___________________________________Period____Date________________
Multi-Step Special Right Triangles
Find the missing side lengths. Leave your answers as radicals in simplest form. 1) 1045°
x45°
2) 745°
x45°
3) 945°
x45°
4) 945°
x45°
5) 5245°
x45°
6) 9645°
x45°
7) 960°
x60°
8) 560°
x60°
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