Triangle Properties 101

Triangle Properties 101

A review of Triangles and their Properties...

I will...

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

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

Open Ended

In as few words as you possibly can, tell me everything you know about triangles... can be anything you remember or have learned previously.

In Review...

• Triangles can be classified by SIDES and by ANGLES

• side labels: equilateral, isosceles, scalene, right, acute, obtuse

• Triangles have 3 sides and 3 angles... hence the name Tri (3) Angles.

• we can use properties of triangles to find missing pieces (this will get a bit more complex as we go.

We use these to help identify various types of triangles... we try to use 1 side descriptor and 1 angle descriptor when classifying triangles. TRIG has to do with various RIGHT triangles, but we will get there shortly.

Multiple Choice

Which would be the best classification for the triangle shown?

• Right Scalene

• Obtuse Equilateral

• Acute Scalene

• Acute Isoscelese

Multiple Choice

Which would be the best classification for the triangle shown?

• right isosceles
• obtuse scalene
• obtuse isosceles
• right scalene

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles

• obtuse scalene

• obtuse isosceles

• acute scalene

Multiple Choice

Which would be the best classification for the triangle shown?

• acute isosceles

• equiangular scalene

• equiangular isosceles

• equiangular equilateral

isosceles Triangles!!

have 2 equal sides AND 2 equal angles...

Multiple Choice

Find the value of y?

• 16

• 12

• 4

• 8

Multiple Choice

The sides of an equilateral triangle have...

• different measures.

• Febtober.

• equal measures.

• 60°.

Multiple Choice

• 12

• 11

• 8

• 6

Multiple Choice

What is the value of x?

• 51
• 49
• 78

Multiple Choice

Find x.

• 180

• 57

• 61.5

• 32.7

Multiple Choice

Find x.

• 180

• 57

• 61.5

• 32.7

Equilateral Triangles

have 3 equal sides and 3 equal angles

Equilateral Triangles

ALL sides are equal... and all angles are equal, which only given them 1 potential measurement because all triangles are = 180 degrees.

180/3 = 60

So every angle in a equilateral triangle is 60 degrees, no matter the size.

Multiple Choice

What is the value of x?

• 16

• 60

• 8

• not enough information

Triangle Sum Theorem

• true for ANY triangle!

• the SUM (add) of all 3 sides ALWAYS equals 180 degrees. ALWAYS...

Find the MISSING ANGLE

Using the Triangle Sum Theorem, we are going to find the missing angles...

we know that all angles = 180

A+B+C=180

so...

34 + 120 + C = 180

154 + C = 180

C = 26

Let's see that agan...

A+B+C=180

so...

52 + 90 + C = 180

142 + C = 180

C = 38

One more time...

This one is a tad trickier...

so, 1st, add up your sides...

(7x+8) + (5x+2) + (7x-1) = 180

then combine like terms...

19x + 9 = 180

19x = 171

x = 9

*now you can find ANY angle!

A= 7(9)+8 = 71

B= 7(9) -1 = 62

C= 5(9)+2 = 47

**and check 71+62+47=180

Multiple Choice

If 2 of the angles of a triangle are 30 and 70 degrees, the third angle measures...

• 80
• 100
• 60
• 90

Multiple Choice

Angles that are exactly 90 degrees are called _____ ______.

• tight angles
• acute angles
• obtuse angles
• right angles

Multiple Choice

Solve for x.

• -12

• -8

• -10

• -5

Multiple Choice

If all three angles are exactly the same measure, how big is each angle?
Hint:    x + x + x  = 180

• 180 degrees
• 90 degrees
• 50 degrees
• 60 degrees

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Multiple Choice

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

• 45°

• 90°

• 180°

• 360°

Multiple Choice

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

• 45°

• 90°

• 180°

• 360°

We can use this to solve:

The ladder is leaning on the ground at a 75º angle. At what angle is the top of the ladder touching the building?

90 + 75 + X = 180

165 + x = 180

x = 15

Multiple Choice

DIG DEEP: If we're looking at an RIGHT triangle, one triangle is 90 degree, so the other two MUST be complementary??

• true

• false

TRUE!

Multiple Choice

In a triangle, how many total degrees are there?

• 100%

• 180 degrees

• it varies

• 360 degrees

Multiple Choice

Find the measure of each angle indicated.

• 139°

• 66°

• 138°

• 116°

Multiple Choice

Solve for x.

• 16

• 11

• 50

• 6