Download 8-3 Special Right Triangles 2-16

2/17/2016
Five-Minute Check (over Lesson 8–2)
CCSS
Then/Now
Theorem 8.8: 45°-45°-90°Triangle Theorem
Example 1: Find the Hypotenuse Length in a 45°-45°-90°
Triangle
Example 2: Find the Leg Lengths in a 45°-45°-90°Triangle
Theorem 8.9: 30°-60°-90°Triangle Theorem
Example 3: Find Lengths in a 30°-60°-90°Triangle
Example 4: Real-World Example: Use Properties of Special
Right Triangles
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Over Lesson 8–2
(1-2) Find x.
Determine whether ∆QRS with vertices
Q(2, –3), R(0, –1), and S(4, –1) is a right triangle.
If so, identify the right angle.
Determine whether the set of numbers can be the
measures of the sides of a triangle. If so, classify
the triangle as acute, obtuse, or right.
16, 30, 33
Over Lesson 8–2
Find x.
A. 5
B.
C.
D. 10.5
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Over Lesson 8–2
Find x.
A.
B.
C. 45
D. 51
Over Lesson 8–2
Determine whether ∆QRS with vertices
Q(2, –3), R(0, –1), and S(4, –1) is a right triangle.
If so, identify the right angle.
A. yes; ∠S
B. yes; ∠Q
C. yes; ∠R
D. no
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Over Lesson 8–2
Determine whether the set of numbers can be the
measures of the sides of a triangle. If so, classify
the triangle as acute, obtuse, or right.
16, 30, 33
A. yes, acute
B. yes, obtuse
C. yes, right
D. no
Over Lesson 8–2
Determine whether the set of numbers can be the
measures of the sides of a triangle. If so, classify
the triangle as acute, obtuse, or right.
A. yes, acute
B. yes, obtuse
C. yes, right
D. no
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Over Lesson 8–2
Which of the following are the lengths of an acute
triangle?
A. 25, 20, 15
1,8
B. 4, 7 __
2
C. 0.7, 2.4, 2.5
D. 36, 48, 62
Content Standards
G.SRT.6 Understand that by similarity, side
ratios in right triangles are properties of the
angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
Mathematical Practices
1 Make sense of problems and persevere in
solving them.
7 Look for and make use of structure.
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You used properties of isosceles and
equilateral triangles.
• Use the properties of 45°-45°-90°triangles.
• Use the properties of 30°-60°-90°triangles.
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Find the Hypotenuse Length in a 45°-45°-90°Triangle
A. Find x.
45°
So:
= • 2
Find the Hypotenuse Length in a 45°-45°-90°Triangle
B. Find x.
45°
45°
Isosceles right triangle thus this is a 45°-45°-90°triangle
So:
= • 2
x = 12
Answer: x = 12
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A. Find x.
A. 3.5
B. 7
C.
D.
B. Find x.
A.
B.
C. 16
D. 32
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Find the Leg Lengths in a 45°-45°-90°Triangle
Find a.
= • 2
Find b.
A.
B. 3
C.
D.
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Find Lengths in a 30°-60°-90°Triangle
Find x and y.
60°
= • 3
= • 2
Answer: x = 4,
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Find BC.
A. 4 in.
B. 8 in.
C.
D. 12 in.
BOOKENDS Genesis designed 2 identical
bookends according to the diagram below. Use
special triangles to find the height of the
bookends.
A.
B. 10
C. 5
D.
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