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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
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