### Section 7 * 2 The Pythagorean theorem & Its converse

```Section 7 – 3
Special Right Triangles
Objectives:
To use the properties of 45-45-90 triangles
To use the properties of 30-60-90 triangles
45-45-90 Triangles
Solve for y in terms of x.
45-45-90 Triangle Theorem
In a 45-45-90 triangle, both legs are
congruent and the length of the hypotenuse
is  times the length of a leg.
=  ∙
=

Example 1
Finding the Length of
the Hypotenuse
Find the value of each variable.
A)
B)
C) Find the length of the hypotenuse of a 4545-90 triangle with legs of length
D) Find the length of the hypotenuse of a 4545-90 triangle with legs of length
Example 2 Finding the Length of a Leg
Find the value of x.
A)
B)
C) Find the length of a leg of a 45-45-90
triangle with a hypotenuse of length 10.
D) Find the length of a leg of a 45-45-90
triangle with a hypotenuse of length 22.
Example 3
Real-World Connection
A) A square garden has sides 100 feet long.
You want to build a brick path along a diagonal
of the square. How long will the path be?
B) The distance from one corner to the
opposite corner of a square playground is 96
feet. To the nearest foot, how long is each side
of the playground?
C) You are designing dinnerware. What is the
length of a side of the smallest square plate on
which a 20-cm chopstick can fit along a
diagonals without any overhang?
Textbook Page 369; # 1 – 11 Odd
Section 7 – 3
Continued…
Objectives:
To use the properties of 30-60-90 triangles
30-60-90 Triangles
Label the sides of the triangle as
HYPOTENUSE, LONG LEG, or SHORT LEG.
30-60-90 Triangle Theorem
In a 30-60-90 triangle, the length of the
hypotenuse is twice the length of the
shorter leg. The length of the longer leg is
times the length of the shorter leg.
=  ∙
=  ∙
Example 4
Finding the Lengths of
the Legs
Find the value of each variable. Leave your
B)
A)
C) Find the lengths of the legs of a 30-60-90
triangle with hypotenuse of length 12.
D) Find the lengths of the legs of a 30-60-90
triangle with hypotenuse of length  .
Example 5
Using the Length of a Leg
Find the value of each variable. Leave your
A)
B)
C) The shorter leg of a 30-60-90 triangle has
length . What are the lengths of the other
two sides?
D) The longer side of a 30-60-90 triangle has
length 18. Find the lengths of the shorter leg
and the hypotenuse.
Homework:
7 – 3 Ditto; 1 – 13
Section 7 – 3
Continued…
Objectives:
To use the properties of 45-45-90 & 30-60-90
triangles
Example 6
Multi-Step Problems
A) The deer warning sign is an equilateral
triangle. Each side is 1 meter long. Find the area of
the sign.
B) A rhombus has 10-inch sides, two of
which meet to form a 30 degree angle. Find the
area of the rhombus.
C) A rhombus has 10-inch sides, two of
which meet to form a 60 degree angle. Find the
area of the rhombus.