Download 4.1 - My Haiku

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 Triangles
Classifications By Sides
• 1. Equilateral Triangles
• Example:
• What does it mean for a triangle to be
equilateral?
• ***All sides must be congruent
Names of Triangles
Classifications 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 Triangles
Classification 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)
• 4)
• 2)
• 5)
• 3)
• 6)
Names of Triangles
Classification by Angles
• 4. Acute Triangle
• Example:
• What do you notice about all of the angles?
• ***An acute triangle has all acute angles
Names of Triangle
Classifications 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 Triangles
Classification 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 Triangles
Classification 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 would
this be?
Right Isosceles Triangle
or
Isosceles Right Triangle
We can name a triangle by
angles 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
A
triangle
• Example:
•
A, B, and C are all
B
C
vertices
• Adjacent Sides – The two sides sharing a
vertex
• AC and AB, AB and BC, AC and BC are adjacent
sides
Parts of Triangles
A
The sides that form the right angle
hypotenuse
AB and BC are the legs of this triangle
leg
The side opposite the right
angle
leg
B
C
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
leg
The non-congruent side of an
isosceles triangle
The congruent sides of an
isosceles triangle
base
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
Think about the angle
sums!!!
67
50
43
90
70
• We can conclude that all the angles add to
180°
40
Triangle Sum Theorem
Exterior Angle Theorem
60
80
90
40
=120
Compare the inside angles
to the outside angle
30
• We can conclude that the sum of the remote
interior angle is equal to the exterior angle
A  B  1
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