Triangles and Angles “I can classify triangles by sides and angles.” “I can find angle measures inside triangles.” By PresenterMedia.comPresenterMedia.com.

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Presentation transcript:

Triangles and Angles “I can classify triangles by sides and angles.” “I can find angle measures inside triangles.” By PresenterMedia.comPresenterMedia.com

By sides Names of Triangles Equilateral All sides  Isosceles 2 sides  Scalene No sides 

By angles Names of Triangles Obtuse 1 obtuse angle Equiangular 3 congruent angles Right 1 right angle Acute 3 acute angles

Mix and Match Use two names to describe this:

Mix and Match Use two names to describe this:

Mix and Match Use two names to describe this:

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

A B C Always label clockwise; always go in alphabetical order.

Anatomy What are the parts called? A corner is called a vertex. Two or more corners are called vertices.

Anatomy What are the parts called? Two sides sharing a common vertex are adjacent. “next to”

Anatomy: Legs Right triangles and isosceles triangles have legs. leg hypotenuse base

Construction workers lay out a right angle Its called the method.

Interior or Exterior Angles Interior Exterior

If you add together all the angles of a triangle, the sum will always be 180 degrees. TST Triangle 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 #1 Watch and take notes 52  27  xx

Teacher Example #2 Watch and take notes 36  (7x + 1)  (x -9) 

Student Practice Do these problems. Solve for x. Find all angles. Classify by name  xx 72  131  xx 17  (x + 24)  (x - 15)  (x + 54)  xx 2x  7x 

1. 24  xx 72  Solve for x. Find all angles. Classify by name.

 xx 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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 proven Corollary to the Triangle Sum Theorem

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

Teacher Example #3 Watch and take notes 52  27  xx

Teacher Example #4 Watch and take notes 38  (7x + 1)  (10x + 9) 

Student Practice Do these problems. Solve for x. Find all angles  71  xx 25  (4x + 1)  (8x + 10) 

49  71  xx 5.

25  (4x + 1)  (8x + 10)  6.6.

“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°x° y°y°

Solve for x. Then find the measure of all angles. Finally, classify the triangle using two names. 72 ° 36 ° x°x° y°y° Solve for x. Then find the measure of all angles. Finally, classify the triangle using two names. 72 ° 36 ° x°x° y°y°