Bell Work Find the measure of the missing variables and state what type of angle relationship they have(alt. interior, alt. ext, same side interior, corresponding).

Bell Work

• Find the measure of the missing variables and state what type of angle relationship they have(alt. interior, alt. ext, same side interior, corresponding).

• 1) 2)

• 3) 4)

Outcomes

• I will be able to:

• 1) Classify a triangle by its sides and/or angles

• 2) Find the measure of interior angles of a triangle using the Triangle Sum Theorem

• 3) Find the exterior angles of a triangle using the Exterior Angle Theorem

Tablet Activity• Download the Geometry Pad app from the

Playstore.

• Do not download anything other than Geometry Pad, as this will slow down the download!!!

• Set your tablet aside, we will use it later!!!

Triangles

• What is a triangle?• Triangle – A polygon formed by three

segments joining three noncollinear points• Example:

• There are two ways to classify triangle:• 1) By its sides• 2) By its angles

Names Of TrianglesClassifications By Sides

• 1. Equilateral Triangles

• Example:

• What does it mean for a triangle to be equilateral?

• ***All sides must be congruent

Names of TrianglesClassifications by Sides

• 2. Isosceles Triangle• Example:

• What does it mean for a triangle to be isosceles?

• ***At least two sides are congruent• ***So, an equilateral triangle is also isosceles

Names of TrianglesClassification by Sides

• 3. Scalene Triangle• Example:

• What does it mean for a triangle to be scalene?

• ***No sides are congruent

Classify the following Triangles

• 1)

• 2)

• 3)

• 4)

• 5)

• 6)

Names of TrianglesClassification by Angles

• 4. Acute Triangle• Example:

• What do you notice about all of the angles?• ***An acute triangle has all acute angles

Names of TriangleClassifications by Angles

• 5. Equiangular Triangle• Example:

• What do you notice about all of the angles?• They are all congruent• ***An equiangular triangle has all angles

congruent• ***An equiangular triangle is also acute.

Names of TrianglesClassification by Angles

• 6. Right Triangle• Example:

• What do you notice about the angles?• There is one right angle• ***There is one right angle in every right

triangle

Names of TrianglesClassification by Angles

• 7. Obtuse Triangles

• Example:

• What do you notice about the angles?• ***There is one obtuse angle in every obtuse

triangle

Classifying Triangles

• When classifying triangles, we can classify them by both their sides and their angles

What type of triangle wouldthis be?

Right Isosceles Triangle orIsosceles Right Triangle

We can name a triangle byangles or sides first

Classifying Triangles Examples

• How would you classify this triangle?

• Obtuse Scalene Triangle

Classifying Triangle Examples

• How would you classify this triangle?

• Acute Scalene Triangle

Parts of Triangles

• Vertex – Each point joining the sides of a triangle

• Example: • A, B, and C are all

vertices• Adjacent Sides – The two sides sharing a

vertex• AC and AB, AB and BC, AC and BC are adjacent

sides

A

BC

Parts of TrianglesA

B C

The sides that form the right angle

AB and BC are the legs of this triangle

The side opposite the rightangle

hypotenuse

leg

leg

Tablet Activity

• Plot the points from each problem and classify the triangles by looking at the measurements of their sides and angles

• See the overhead on how to use the app and the answers for #1!!!

Parts of Triangles

The non-congruent side of anisosceles triangle

baseThe congruent sides of anisosceles triangle

leg

leg

Types of Angles in Triangles

• There are both interior and exterior angles we are concerned with when looking at triangles

• Interior angle are inside the triangle

• Exterior angles are outside the triangle

Triangle Sum

• We can conclude that all the angles add to 180°

Think about the angle sums!!!

43

67

70

90

50

40

Triangle Sum Theorem

Exterior Angle Theorem

• We can conclude that the sum of the remote interior angle is equal to the exterior angle

1 BA

=120

80

4090

60

30Compare the inside anglesto the outside angle

Exterior Angle Theorem

Examples

• How can we solve this?

• 42 + 90 + x = 180• 132 + x = 180• -132 -132• x = 48

Examples

• How can we solve this?• x+ 110 = 4x – 7• -x -x• 110 = 3x – 7• +7 +7• 117 = 3x• 39 = x

Examples• How can we solve this?• Remember, we can

label things we know even if they are not in our picture.

• Now we have,• 33 + x + 90 = 180• 123 + x = 180• -123 -123• x = 57

90

Examples• How can we solve this?

• x + x + 30 = 180• 2x + 30 = 180• - 30 - 30• 2x = 150• x = 75

Independent Practice• 1) Solve for the missing variable• 2) Circle the chart

• r + 53 + 37 = 180• r + 90 = 180• r = 90