Download Triangles - Skyline R2 School

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Objective
Identify and classify triangles
Vocabulary
Triangle
A polygon that has three sides and three
angles
Vocabulary
Acute triangle
A triangle having three acute angles
Vocabulary
Right triangle
A triangle having one right angle
Vocabulary
Obtuse triangle
A triangle having one obtuse angle
Vocabulary
Congruent segments
Sides of a triangle having the same length
Vocabulary
Scalene triangle
A triangle having no congruent sides
Vocabulary
Isosceles triangle
A triangle having at least two congruent sides
Vocabulary
Equilateral triangle
A triangle having three congruent sides
Example 1 Find Angle Measures of Triangles
Example 2 Find a Missing Measure
Example 3 Classify Triangles
Example 4 Classify Triangles
PLANES An airplane has wings
that are shaped like triangles.
Find the missing measure.
x0 + 1120 + 470 = 1800
The sum of the measures is 1800
Add angles together
Remember: sum = 1800
1/4
PLANES An airplane has wings
that are shaped like triangles.
Find the missing measure.
Bring down x0
x0 + 1120 + 470 = 1800
Combine “like” terms
x0 + 1590 = 1800
Bring down = 1800
Ask “what is being done to the
variable?”
The variable is being added
by 1590
Do the inverse on both sides
of the equal sign
1/4
PLANES An airplane has wings
that are shaped like triangles.
Find the missing measure.
Bring down x0 + 1590
x0 + 1120 + 470 = 1800
x0
+
1590 =
1800
Subtract 1590
Bring down = 1800
x0 + 1590 - 1590 = 1800 - 1590
x0 + 00 =
Subtract 1590
Bring down x0
Combine “like” terms
Bring down =
1/4
PLANES An airplane has wings
that are shaped like triangles.
Find the missing measure.
x0 + 1120 + 470 = 1800
x0
+
1590 =
1800
Combine “like” terms
Use the Identify Property to
add x0 + 00
x0 + 1590 - 1590 = 1800 - 1590
x0 + 00 = 210
Answer:
x = 210
1/4
SEWING A piece of fabric is shaped like a triangle.
Find the missing measure.
x
Answer:
x = 49
1/4
ALGEBRA Find mA in ABC if mA
mC 80.
mB and
x
Draw the triangle
Define mA as x
mA  mB
2/4
ALGEBRA Find mA in ABC if mA
mC 80.
mB and
2x
Since mA is x and m   mB
then B can also be x
x + x = 2x
The sum of the measures is 1800
2/4
ALGEBRA Find mA in ABC if mA
mC 80.
mB and
2 x + 800 = 1800
Add 800 for the mC
Put the = 1800 since this is the
sum
Solve for the unknown
2/4
ALGEBRA Find mA in ABC if mA mB and
mC 80.
Ask “what is being done to the
variable term (2x)?”
2 x + 800 = 1800
2x + 800 - 800 = 1800 - 800
The variable term is being
added by 800
Do the inverse on both sides
of the equal sign
Bring down 2x + 800
Subtract 800
Bring down = 1800
Subtract 800
2/4
ALGEBRA Find mA in ABC if mA mB and
mC 80.
Bring down 2x
0
0
2 x + 80 = 180
Combine “like” terms
0
0
0
2x + 80 - 80 = 1800 - 80
Bring down =
0
0
2x + 0 = 100
Combine “like” terms
2x = 1000
Use the Identify Property to
add 2x + 00
Ask “what is being done to the
variable?”
The variable is being
multiplied by 2
2/4
ALGEBRA Find mA in ABC if mA mB and
mC 80.
Do the inverse on both sides
of the equal sign
2 x + 800 = 1800
0
Bring
down
2x
=
100
0
0
0
0
2x + 80 - 80 = 180 - 80
Using the fraction bar, divide
0
0
2x + 0 = 100
both sides by 2
0
2x = 100
Combine “like” terms
2x = 1000
2
2
Use the Identify Property to
multiply 1  x
1  x = 500
x = 500
Answer:
mA = 500
Since you defined mA as x
and x = 500 then mA = 500
2/4
ALGEBRA Find mJ in JKL if mJ mK and
mL 100. Draw the triangle then solve
Answer: mJ = 40
2/4
Classify the triangle by its angles and its sides.
Obtuse
All triangles have 3 names
First, middle and last (just like you)
First: classify angle
One angle greater than 900 meets
the definition of obtuse angle
3/4
Classify the triangle by its angles and its sides.
Answer:
Obtuse Isosceles Triangle
Next, classify by sides
2 sides congruent meets the
definition of isosceles
All triangles have the last name as
“triangle”
3/4
Classify the triangle by its angles and its sides.
Answer: Right Scalene Triangle
3/4
Classify the triangle by its angles and its sides.
Acute
All triangles have 3 names
First, middle and last (just like you)
First: classify angle
All angles are less than 900 meets
the definition of acute angle
4/4
Classify the triangle by its angles and its sides.
Answer:
Acute Scalene Triangle
Next, classify by sides
No sides have a congruent symbol
so meets the definition of scalene
All triangles have the last name as
“triangle”
4/4
*
Classify the triangle by its angles and its sides.
Answer: Acute Equilateral Triangle
4/4
Assignment
Lesson 10:4
Triangles
3 - 24 All