Download Triangles and Angles

Triangles and Angles
Classifying Triangles
• Line segments are congruent if they have
the same length
• One way to classify triangles is by the
number of congruent sides they have
Classifying Triangles
• Scalene Triangles have no congruent
sides
• Isosceles Triangles have two congruent
sides
• Equilateral Triangles have three congruent
sides
Classifying Triangles
• Another way to classify triangles is by the
measure of their angles
• Acute Triangles have three acute angles
• Obtuse Triangles have one obtuse angle
• Right Triangles have one right angle
Classifying Triangles Checkpoint
• Classify each angle by it’s sides and it’s
angles:
Angle: Acute
Angle:
Obtuse
Angle:
Right
Side:
Side:
Scalene
Side:
Isosceles
Equilateral
Interior Angles of a Triangle
The sum of the measures of the angles of a
triangle is 180
Triangle Mini-Lab
Materials Needed:
• Pencil
• Ruler (share with a neighbor)
• Scissors (share with a neighbor)
• Protractor
Triangle Mini-Lab
• Using a ruler and pencil, draw any large
triangle and cut it out with scissors.
• Individually label each angle 1, 2, and 3.
• Tear off (do NOT cut) a large section of
each angle and arrange so each vertex is
touching and each angle is adjacent to the
next.
Triangle Mini-Lab
• What type of angle did the three angles
form when placed together?
A straight angle
• What is the measure of this angle?
180 degrees
• Let’s confirm….
Triangle Mini-Lab
• Flip over one angle and use your
protractor to measure it.
• Write the measure on the back of the
angle and repeat these steps for the other
two angles.
• Add up the measures of each of the
angles.
Finding The Measures of Angles
• In an equilateral triangle, all of the sides
are congruent and all of the angle
measurements are congruent
• What is the measure of each angle?
Finding The Measures of Angles
What do we know?
• We know that each angle is congruent but we
don’t know their measure. Let’s call it “X.”
• We know that all three angles add up to 180
degrees. Therefore, X + X + X = 180
• What is the measure of each angle?
3x = 180
X = 60
Finding The Measures of Angles
Checkpoint
Find the measure of each triangle then
classify the triangle by it’s angles:
m
m
m
a = 46,
b = 42,
c = x + 46 + 42 = 180
x + 88 = 180
x = 92
Classify: Obtuse
Finding The Measures of Angles
Checkpoint
Find the measure of each triangle then
classify the triangle by it’s angles:
m
m
m
a = 3x,
b = 2x,
c=x
3 x 30 = 90
2 x 30 = 60
x = 30
x + 2x + 3x = 180
6x = 180
x = 30
Classify: Right
Finding The Measures of Angles
Checkpoint
Find the measure of each triangle then
classify the triangle by it’s angles:
m
m
m
a = 4x,
b = 3x,
c = 2x
4 x 20 = 80
3 x 20 = 60
2 x 20 = 40
4x + 3x + 2x = 180
9x = 180
x = 20
Classify: Acute
Homework
• Skill 6: Triangles (both sides)
• 6-2 Practice Skills: Triangles and Angles
(both sides)
• Due Tomorrow!