Thurs, 3/6
SWBAT… classify triangles in the coordinate plane
Agenda
1.
Warm-up: (10 min)
2.
Classifying triangles (40 min)
Warm-Up:
1. Write your HW in your planners
Homework:
Isosceles and Equilateral Triangles
#1 – #8
#9: Is the triangle scalene, isosceles, or equilateral
A(0, 1), B(4, 1), C(7, 0)
Unit 5:
Classifying Triangles
Classification means
put things into a
group according to
how they are alike.
We will break this group of
animals into smaller groups.
The same animals can be put into
different groups depending on what
we look at when we classify them.
Today you will learn how
triangles can be classified
in two different ways...
Think of all the different kinds
of triangles you know.
Did you come up with all of these?
Acute
Obtuse
Right
Scalene
Isosceles
Equilateral
Triangle

A polygon with 3 angles and 3 straight sides.
 The
three endpoints are called vertices.
Classifying by side lengths
Scalene
Isosceles
Equilateral
Scalene Triangle
 All
sides are different lengths.
Isosceles Triangle
 Two
out of the three sides are
equal lengths.
Isosceles Triangle Theorem

If two sides of a triangle are congruent, then
the angles opposite those sides are
congruent.
Ex. If AC = BC, name two congruent angles.
Equilateral Triangle
 All
sides have the same length
Properties of Equilateral Triangles

A triangle is equilateral if and only if it is has
three congruent angles (all the measures
would then be 600.)
Ex. KLM is an equilateral triangle with
KL = d + 2, LM = 12 – d, KM = 4d – 13.
Find d and the measure of each side.
4d – 13 = d + 2 Substitution
3d – 13 = 2 Subtract d from each side.
3d = 15 Add 13 to each side.
d = 5 Divide each side by 3.
KL = 7, LM = 7, KM = 7
Classify this triangle by its sides.
Classify this triangle by its sides.
Classify this triangle by its sides.
Classify the following triangles by
their sides. Use these signals:
Scalene
Isosceles
Equilateral
Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral
Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral
Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

What formula do you use to determine if a
triangle is scalene, isosceles, or
equilateral?
Answer: The terms scalene, isosceles, and
equilateral have to do with side lengths of a
triangle so you use the Distance Formula.
Classifying by angle measures
Right
Acute
Obtuse
Acute Triangle
All three angles are less than 900.
800
400 600
Obtuse Triangle
One of the three angles is more than 900
200
1300
300
Right Triangle
One of the three angles is exactly 900
Classify the following triangles by
their sides. Use these signals:
Acute
Obtuse
Right
Classify by angles.
Acute
Obtuse
Right
Classify by angles.
1000
Acute
Obtuse
Right
Classify by angles.
850
450
500
Acute
Obtuse
Right
B
A
D
C
E
Now you should be able to classify
any triangle by both its side
lengths and its angles.
Classify the triangles by sides lengths
and angles
a)
b)
7
c)
40°
15°
25
24
70°
70°
120°
Solutions:
a) Scalene, Right
b) Isosceles, Acute
c) Scalene, Obtuse
45°
Example 1
Classify a triangle in a coordinate plane
Determine whether PQO with
vertices at P(-1, 2), Q(6, 3), O(0, 0),
is scalene, isosceles, or
equilateral. Explain.
SOLUTION Use the distance formula to find the side lengths.
OP =
=
( x2 – x1 ) 2 + ( y2 – y1 ) 2
( (– 1 ) – 0 ) 2 + ( 2 – 0 ) 2 =
5
2.2
=
45
6.7
( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 =
50
7.1
OQ =
( x2 – x1 ) 2 + ( y2 – y1 ) 2
=
PQ =
( 6 – 0 )2 + ( 3 – 0 )2
( x2 – x1 ) 2 + ( y2 – y1 ) 2
=
EXAMPLE
Explanation
Classify a triangle in a coordinate plane (continued)
PQO is a scalene triangle since none
of the sides are congruent.
HW: Isosceles and Equilateral Triangles
#1 – #8
#9: Is ABC scalene, isosceles,
or equilateral A(0, 1), B(4, 1), C(7, 0)
 Using
the ruler, draw triangles with
the following side measures:
a.) 3cm, 4cm, 6cm
b.) 2cm, 2cm, 6cm
Triangle Inequality Theorem

The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.

Ex: Can these be the measures of a triangle?
a.) 3cm, 4cm, 6cm
b.) 2cm, 2cm, 6cm
Example: Find value of x and
missing side measurement
Ex. Find the measure of each side of
equilateral  RST with RS = 2x + 2, ST = 3x,
and TR = 5x – 4.
5x – 4 = 2x + 2
x=2
RS = 6
ST = 6
TR = 6
Ex. Find the measure of each side of
isosceles  ABC with AB = BC if AB = 4y,
BC = 3y + 2, and AC = 3y.
3y + 2 = 4y
y=2
AB = 8
BC = 8
AC = 6
Ex. Find x of isosceles right  WZY if angle
YWZ = 900, WZ = WY, and WYZ = 3x.
3x + 3x + 90 = 180
x = 15
Example: Find missing angle
measurements
Ex: Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, BCE, BDE, CDE, ACD, ABD
c. equilateral triangles
Answer: None!
Exit Slip
Is triangle A(0, 1), B(4, 4), and C(7,0)
scalene, isosceles or equilateral. Explain.
Answer:
AB = 5
BC = 5
CA = 7.1
Since AB = Triangle ABC is isosceles since two
of the sides are congruent.
#1 – #4: Find x:
1.)
2.)
6x0
3.)
600
3x + 8
4x – 4
400
2x0
4.)
(4x – 5)0
5.) Is triangle A(0, 1), B(4, 4), and C(7,0)
scalene, isosceles or equilateral. Explain.
SWBAT… classify triangles in the coordinate plane
Mon, 3/10
Agenda
1.
Warm-up: (10 min)
2.
4 Examples (25 min)
3.
Review HW (10 min)
Warm-Up: Find the missing angles:
HW: Re-do 5 problems - Worksheet
Warm-Up: What is Congruent?
1. AB  ________
2. BD  _______  _______  _______
3. CBE  ________  BCE
4. BDE  ________
5. ABC  ________
Example: Find missing angle
measurements
Name the missing coordinates of
isosceles right triangle ABC.
Answer: C(0, 0); A(0, d)
Name the missing coordinates of
isosceles right triangle SRQ.
Answer: Q(0, 0); S(c, c)
Find the missing angles.
Warm-Up: Find the missing angles.
Warm-Up
Find the missing angles.
Warm-Up:
Find the missing angles.
Homework: Collected.
What do you know about the
Pythagorean Theorem?
1.
a)
b)
c)
Formula?
When and why it’s used?
Solve for x: