5.1 - Tring Intro pt.2

5.1 - Tring Intro pt.2

Right triangles and exterior angle theorems

I will:

• prove the triangle angle sum theorem and the exterior angle theorem.

• use relationships in triangles, such as the triangle angle sum theorem and the exterior angle theorem, to solve problems

REVIEW!!

Isosceles and angle sum theorem

Multiple Choice

The sides of an equilateral triangle have...

• different measures.

• Febtober.

• equal measures.

• 60°.

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

Multiple Choice

Solve for x.

• 16
• 11
• 50
• 6

Multiple Choice

What is the measure of the missing angle?

• 82
• 43
• 55
• 180

Multiple Choice

Find the measure of the indicated angle. 

• 145 degrees
• 24 degrees
• 20 degrees 
• 21 degrees

Exterior Angle Theorem

tells us that the exterior angle on a triangle is equal to the 2 opposite inside angles.

this is because the two angles C and D are supplementary (=180) and A,B, and C are supplementary as well because we learned that all angles in a triangle are 180 degrees.

so d HAS TO EQUAL a and b.

Let's review how to use it...

so... a+b=d

63 + 86 = x

so... x = 149.

that's it...

Another example...

a+b=d

80 + x = 145

x=65

a+b=d

(5y+3) + (4y+8) = 146

9y + 11 = 146

9y = 135

y = 15

a = 5(15)+3 = 75+3 = 78

b = 4(15)+8 = 60-8 = 52

Multiple Choice

Which of the following angles can you add together to equal angle d?

• Angle a and Angle b

• Angle b and Angle c

• Angle a and Angle c

• Angle a and Angle b and Angle c

Multiple Choice

Which of the following terms best describes Angle d?

• Remote interior angle

• Corresponding angle

• Exterior angle

• Interior angle

Multiple Choice

Find the measure of angle x.

• 138
• 96
• 93
• 87

Multiple Choice

What is the measure of angle b?

• 36^o

• 56^o

• 63^o

• 117^o

Multiple Choice

Find the measure of the indicated angle. 

• 95
• 85
• 35
• 45

Pythagorean Theorem

finding missing pieces from a right triangle.

PARTS of a RIGHT Triangle

We have angles A, B, and C, which gives us our side lengths. C being the hypotenuse, a and b being our "legs."

**right angle uses sides a and b, and hypotenuse is ALWAYS c.

a²+b²=c²

• the sum of the square of two legs of a triangle equals the square of the hypotenuse.

• HOW TO SOLVE

• 1. pick out the numbers for the side lengths you know, plus them in and solve. ... that's it.