Loading...

PPT – Special Cases, for Right Triangles PowerPoint presentation | free to download - id: 78f562-NzIwM

The Adobe Flash plugin is needed to view this content

Special Cases, for Right Triangles 30 60 90

Triangles

60

30

45

45 45 90 Triangles

45

1. An equilateral triangle is also equiangular,

all angles are the same.

60

2

2. Lets draw an Altitude from one of the

vertices. Which

is also a Median and Angle bisector.

30

60

2

30

3. The bisected side is divided into two equal

segments and the bisected angle has now two 30

equal angles.

2

60

- Congratulations! Two
- 30 60 90 triangles have just been born
- Oooh and you watched!!!!

Lets separate the top triangle and label the

unknown side as z.

apply the Pythagorean Theorem to find the unknown

side.

1

-1 -1

z

When, the smallest side is equal to 1, the

hypotenuse is 2 times as big, 1 2 2 And the

other leg is times as big, 1

Can we generalize this result for all

30-60-90 right triangles?

60

(2)

2

4

2

1

(2)

Yes it works!

30

(2)

Is this true for a triangle that is twice as big?

Is this true for a triangle that is half the

original size?

Yes , it still works. If we know 1 side length

of a 30-60-90 triangle, we can use this pattern

to find the other 2 sides

60

2

30

In a 30-60-90 triangle, the hypotenuse is

twice as long as the shorter leg, and the longer

leg is times as long as the shorter leg.

Find the values of the variables. Round your

answers to the nearest hundredth.

y

2x 14

30

2x 14

x

2 2

14

60

x 2

Is this 30-60-90?

90-3060

Then we know that

Find the values of the variables. Round your

answers to the nearest unit.

2x y

30

y

90

.

OR

60

x

x

Is this a 30-60-90?

90-6030

OR

Find the values of the variables. Find the exact

answer.

x

2x y

60

y

.

30

30

x

Is this a 30-60-90?

90-6030

Lets draw a diagonal for the square. The

diagonal bisects the right angles of the square.

What kind of right triangles are formed?

y

The triangles are 45-45-90

Lets draw the bottom triangle and label the

hypotenuse as y

Lets apply the Pythagorean Theorem to find the

hypotenuse.

45-45-90 Right Triangle

x

x

Can we generalize our findings?

In a 45-45-90 triangle, the hypotenuse is

times as long as a leg And both legs are the

same size.

45

s

s

45

s

Find the values of the variables. Round your

answers to the nearest tenth.

45

36

x

If y x

.

then

45

OR

x

y

Is this a 45-45-90?

90-4545

OR

Find the values of the variables. Give an exact

answer.

45

42

x

If y x

.

then

45

x

y

Is this a 45-45-90?

90-4545

Find the values of the variables. Give the exact

answer.

x 21

45

y

x

45

21

Is this a 45-45-90?

90-4545