Download Geometry 7.4 45-45-90 and 30-60-90 Triangles

Geometry 7.4 45­45­90 and 30­60­90 Triangles
Big Idea
What is a 45-45-90 triangle?
What is a 30-60-90 triangle?
Why are they called "special" right
triangles?
How are the sides related to each other in a
45-45-90 triangle and a 30-60-90 triangle?
How can we use these relationships to find
missing side length?
April 11, 2016
Agenda
­ Warm­Up ­ 7.4 Special Right Triangles ­ Investigation + Practice
­ HW #7.4
­ Return quizzes
Warm­Up
Simplify the following:
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
You now will be completing an investigation in your groups.
Each group member has a different triangle but they all have a
pattern between their sides.
Your goal is to figure out this pattern.
x
10
10
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
You now will be completing a second investigation in your groups.
Each group member has a different triangle but they all have a
pattern between their sides.
Your goal is to figure out this pattern.
Key Vocabulary (parts of a right triangle):
short leg
leg
hypotenuse
hypotenuse
long leg
leg
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
Big Idea - How are the sides of a 30-60-90 triangle related to each
other? How can we use these patterns to find the lengths of
missing sides?
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
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12
12
x
6
6
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
Let's add these patterns to our theorem/postulate list...
hypotenuse
If
then
45­45­90 Triangle
If
short leg
hypotenuse
then
long leg
30­60­90 Triangle
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
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Geometry 7.4 45­45­90 and 30­60­90 Triangles
April 11, 2016
Exit Slip #7.4 - one paper per person. Do individually...
1) Find the value of x in each of the 45­45­90 triangles below.
Use the patterns of 45­45­90 triangles and 30­60­90 triangles rather than the Pythagorean Theorem
2) Find the values of x and y in each of the 30­60­90 triangles below.
#7.4 (PW)p.133: 1­12 (good practice) 45­45­90 and 30­60­90 Triangles
or p.134: 15­20 (challenge)
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