Triangles and Angles

“I can classify triangles by sides and angles.”“I can find angle measures inside triangles.”

By PresenterMedia.com

By sidesNames of Triangles

EquilateralAll sides

Isosceles2 sides

ScaleneNo sides

By anglesNames of Triangles

Obtuse1 obtuse angle

Equiangular3 congruent

angles

Right1 right angle

Acute3 acute angles

Mix and MatchUse two names to describe this:

Mix and MatchUse two names to describe this:

Mix and MatchUse two names to describe this:

It can be proven:Equilateral triangles are always equiangular;And equiangular triangles are always equilateral.

In general, a triangle is named by its vertices.This one is called :

A

BC

Always label clockwise; always go in alphabetical order.

AnatomyWhat are the parts called?

A corner is called a vertex.

Two or more corners are called vertices.

AnatomyWhat are the parts called?

Two sides sharing a common vertex are adjacent.“next to”

Anatomy: LegsRight triangles and isosceles triangles have legs.

leg

legleg leg

hypotenuse

base

Construction workers lay out a right angleIts called the 3-4-5 method.

Interior or Exterior Angles

Interior Exterior

If you add together all the angles of a triangle,the sum will always be 180 degrees.

TSTTriangle Sum Theorem

In other words…If you know 2 angles of a triangle, you can always find the third.

“Proof”Convincing argument why it must be true.

Teacher Example #1Watch and take notes

52

27 x

Teacher Example #2Watch and take notes

36

(7x + 1) (x -9)

Student PracticeDo these problems. Solve for x. Find all angles. Classify by name.

1. 2.

3. 4.

24

x 72

131x

17

(x + 24)

(x - 15)(x + 54)

x

2x

7x

1.

24

x 72

Solve for x. Find all angles. Classify by name.

2.

131x

17

Solve for x. Find all angles. Classify by name.

3. (x + 24)

(x - 15)

(x + 54)

Solve for x. Find all angles. Classify by name.

4. x

2x

7x

Solve for x. Find all angles. Classify by name.

In a right triangle, the two acute angles add up to 90.

Corollary = a statement easily provenCorollary to the Triangle Sum Theorem

An exterior angle is equal to the sum of the two interior angles not adjacent to it.

EATExterior Angle Theorem

Teacher Example #3Watch and take notes

52

27 x

Teacher Example #4Watch and take notes

38

(7x + 1) (10x + 9)

Student PracticeDo these problems. Solve for x. Find all angles.

5. 6.

49

71 x

25

(4x + 1) (8x + 10)

49

71 x

5.

25

(4x + 1) (8x + 10)

6.

• “I can classify triangles by sides and angles.”• “I can find angle measures inside triangles.”

Solve for x. Then find the measure of all angles. Finally, classify the triangle using two names.

72°

36°

x°y°

Solve for x. Then find the measure of all angles. Finally, classify the triangle using two names.

72°

36°

x°y°

Solve for x. Then find the measure of all angles. Finally, classify the triangle using two names.

72°

36°

x°y°