Special Right Triangles

Special Right Triangles

Take notes, you'll turn them in!

Yes, let's talk about the Special Right Triangles

• The video slides are "trimmed". Watch only the parts that play, don't rewind to far. Most of them stop before the "end".

• You don't have to watch other parts that don't automatically play.

The 30-60-90

• The hypotenuse is exactly double the shortest leg

• This explains the

   $1:2:\sqrt{3}$   relationship

• The 1 is the shortest leg

• The  $\sqrt{3}$  is the "middle leg"

• The 2 is the hypotenuse

The 45-45-90

• Isosceles --> 2 equal legs

• 45-45-90 --> 2 equal angles (due to isosceles)

• In a

   $1:1:\sqrt{2}$  ratio

• The 1:1 part signifies that the "legs" are congruent

Use your notes to answer the questions that follow in the next slides.

• These triangles are special, one of the 2 aforementioned.

• None of these are dilated...yet.

Multiple Choice

What type of special triangle is this?

• 45°-45°-90°
• 30°-60°-90°
• Equiangular
• Equilateral

Multiple Choice

What type of special triangle is this?

• 45°-45°-90°
• 30°-60°-90°
• Isosceles
• Obtuse

Multiple Choice

Find x.

• 90°
• 45°
• 30°
• 60°

Multiple Choice

Which special right triangle is isosceles?

• the 30 - 60 - 90

• the 45 - 45 - 90

• the equilateral triangle

• none of these is isosceles

Multiple Choice

Which special right triangle has a hypotenuse that is exactly twice as long as the shortest leg?

• the 45 - 45 - 90

• the 30 - 60 - 90

• an isosceles right triangle

• a scalene right triangle

Fill in the Blanks

Find the measure of side h:

Fill in the Blanks

Find the measure of side x:

Multiple Choice

Find the value of the missing angle:

• 45

• 30

• 120

• not possible

Multiple Choice

Find x.

• 90°
• 45°
• 30°
• 60°

Fill in the Blanks

Find the measure of angle B (in degrees):

Fill in the Blanks

Find the measure of side x:

Multiple Choice

Which of the following MUST be true for the triangle pictured?

• angle A > angle B

• angle A < angle B

• angle A = angle B

• none of these

Multiple Choice

Find the value of side h:

• $1$

• $2$

• $\sqrt{2}$

• $\sqrt{3}$

Multiple Choice

Find the measure of side y:

• 1

• 2

• $\sqrt{3}$

• $\sqrt{2}$

The next video...seems kinda long!

• The next video contains dilated versions of these special right triangles.

• The ratios hold up, the triangle has just been multiplied by a scale factor.

• If you catch onto what is happening early on, feel free to move ahead to the last questions of this lesson.

Multiple Choice

What type of special right triangle is this?

• Isoceles right
• 30-60-90
• not a special right triangle

Multiple Choice

Find x.

• 12
• √2
• √3
• 6

Multiple Choice

Find x.

• 10
• √3
• 5
• 10√3

Multiple Choice

Find x.

• 30°
• 45°
• 60°
• 90°

Multiple Choice

Find x.

• 10
• 20
• 10√3
• √3

Multiple Choice

What is the measure of side c?

• 7
• 7/√2
• 7√2
• 14

Multiple Choice

Find a.

• 2

• 4

• $2\sqrt{2}$

• $2\sqrt{2}\sqrt{2}$