# Chapter 7.4 Notes: Special Right Triangles - PowerPoint PPT Presentation

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## Chapter 7.4 Notes: Special Right Triangles

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### Chapter 7.4 Notes: Special Right Triangles Goal: You will use the relationships among the sides in special right triangles. Part I: Draw an isosceles right triangle. – PowerPoint PPT presentation

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Title: Chapter 7.4 Notes: Special Right Triangles

1
Chapter 7.4 Notes Special Right Triangles
• Goal You will use the relationships among the
sides in special right triangles.

2
• Part I
• Draw an isosceles right triangle.
• What do you know about the two legs?
• What do you know about the measures of the acute
angles of an isosceles right triangle?
• Another name for an isosceles right triangle is a
• 45o-45o-90o triangle.

3
• Theorem 7.8 45o-45o-90o Triangle Theorem
• In a 45o-45o-90o triangle, the hypotenuse is
• times as long as each leg.
• hypotenuse ________________
• Find the length of the hypotenuse.
• Ex.1 Ex.2

4
• Find the lengths of the legs in the triangle.
• Ex.3 Ex.4

• 2
• Part II
• Draw an equilateral triangle with side length of
6 cm
• What do you know about an equilateral triangle?
• 1. ________________________________
• 2. ________________________________

5
• When you divide an equilateral triangle in half,
the two triangles formed are called a 30o-60o-90o
triangle.
• Theorem 7.9 30o-60o-90o Triangle Theorem
• In a 30o-60o-90o triangle, the hypotenuse is
twice as long as the shorter leg, and the longer
leg is
• times as long as the shorter leg.
• hypotenuse _______________
• longer leg ________________

6
• Ex.5 Find the values of x and y. Write your
• Find the value of the variable.
• Ex.6 Ex.7
• 60o
• y

• 30o
• x

7
• Ex.8 The shorter leg of a 30-60-90 triangle has
a length of . What are the lengths of the
other two sides?
• Ex.9 A baseball diamond is a square. The
distance from base to base is 90 feet. How far
does the second baseman throw a ball to home
plate?

8
• Find the value of the variable.
• Ex.10 Ex.11
• Ex.12
• 60o

• b
• a

• 15