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Lesson 7.3 Two Special Right Triangles

- Objectives
- To use properties of 45-45-90 triangles
- To use properties of 30-60-90 triangles

Isosceles Right Triangle Theorem

ISOSCELES RIGHT TRIANGLE THEOREM In an

isosceles right triangle, if the legs have

length, l, then the hypotenuse has length ____.

NOTE If you are given the length of the

hypotenuse, you can determine the length of a

side by dividing it by_________________________ __

_________________________.

l v2

v2, then rationalizing the denominator, when

necessary.

EXAMPLES Find the length of the hypotenuse

in each isosceles triangle below.

3v2

4v2

5v2

6v2

7v2

12v2

Recall Triangle Inequalities

- If two angles of a triangle are not congruent,

then the longest side lies opposite the _______

angle and the shortest side lies opposite the

________ angle.

largest

smallest

30-60-90 TRIANGLE THEOREM

30-60-90 TRIANGLE THEOREM In a 30-60-90

triangle, if the side opposite the 30 degree

angle has length, l, the hypotenuse has

length _______. NOTE These triangles are

sometimes referred to as 1-2-v3 right

triangles.

2l

Easy way to remember the relationship among

angles and sides in 30-60-90 triangles

- 1. Rank order the following numbers from

smallest to largest - 1, 2, v3
- 2. Now, use the Triangle
- Inequality Theorem to
- place the side
- lengths 1l, v3l , 2l
- opposite the
- appropriate angles in a
- 30-60-90 triangle.

60

2l

1l

1, v3 , 2

30

lv3

NOTE It is usually easier to determine the

length of the shortest and longest sides,

initially.

Find the length of each indicated side

60

____

____

30

____

NOTE The length of one side will be provided by

your instructor.

Find the length of each indicated side.

In summary

Pythagorean Primitives 3 4 5 5 12 13 8

15 17 7 24 25

and their multiples!

- We can find the lengths of sides in right

triangles by using

c a

b Pythagorean Theorem c2 a2 b2

30-60-90 ? 30 2l lv3

60 l

45-45-90 ? l

45 l lv2 45

Putting it all together

Find the length of each indicated side.

20v3

8 __ __

5 40

20

8 3

8 4

Homework Assignment

- Special Right Triangles WS (1-10 all, 12)