7-6 Triangles
Learn to classify triangles by their side
lengths and angle measures.
Course 2
7-6 Triangles
Insert Lesson Title Here
Vocabulary
scalene triangle
isosceles triangle
equilateral triangle
acute triangle
obtuse triangle
right triangle
Course 2
7-6 Triangles
One way to classify triangles is by the lengths of
their sides.
Triangles classified by sides
A scalene triangle
has no congruent sides.
Course 2
7-6 Triangles
One way to classify triangles is by the lengths of
their sides.
Triangles classified by sides
An isosceles triangle
has at least 2 congruent sides
Course 2
7-6 Triangles
One way to classify triangles is by the lengths of
their sides.
Triangles classified by sides
In an equilateral triangle, all of the
sides are congruent.
Course 2
7-6 Triangles
One way to classify triangles is by the lengths of
their sides. Another way is by the measures of
their angles.
Triangles classified by angles
In an acute triangle, all of the
angles are acute.
Course 2
7-6 Triangles
One way to classify triangles is by the lengths of
their sides. Another way is by the measures of
their angles.
Triangles classified by angles
An obtuse triangle has
one obtuse angle.
Course 2
7-6 Triangles
One way to classify triangles is by the lengths of
their sides. Another way is by the measures of
their angles.
Triangles classified by angles
A right triangle
has one right angle.
Course 2
7-6 Triangles
Writing Math
When classifying a triangle according to its
sides and angles, use the word that describes
the sides first, and use the word that
describes its angles second.
Course 2
7-6 Triangles
Additional Example 1A & 1B: Classifying Triangles
Classify each triangle according to its sides
and angles.
A. isosceles Two congruent sides
acute
Three acute angles
5 ft
9 ft
9 ft
This is an isosceles acute triangle.
B. scalene
right
No congruent sides
One right angle
This is a scalene right triangle.
Course 2
24 m
25 m
7m
7-6 Triangles
Additional Example 1C & 1D: Classifying Triangles
Classify each triangle according to its sides
and angles.
C. scalene
No congruent sides
acute
Three acute angles
This is a scalene acute triangle.
D. equilateral Three congruent sides
acute
Three acute angles
This is an equilateral acute triangle.
Course 2
7-6 Triangles
Additional Example 2: Identifying Triangles
Identify the different types of triangles in the
figure, and determine how many of each there are.
Course 2
Type
How many
Name
Scalene
2
ABD,
BCD
Isosceles
2
ACE,
ABC
Right
2
ABD,
BCD
Obtuse
1
ACE
Acute
1
ABC
7-6 Insert
Lesson Title Here
Triangles
Try This: Example 2
Identify the different types of triangles in the
figure, and determine how many of each there are.
A
I
B
J
D
H
G
Course 2
C
Type
Isosceles
F
How many
5
E
Name
DJA,
JDG
HJI,
BCD
DFE
Obtuse
2
DJA,
ADG
Acute
4
JDG,
JHI,
BCD,
DEF
7-6 Triangles
Insert Lesson Title Here
Lesson Quiz
Classify each triangle according to its side or
angle measures.
1. 7ft, 8ft, 12ft
scalene
2. 45°, 90°, 45° right
3. 12, 9, 12 isosceles
4. 120°, 20°, 40° obtuse
5. Identify the different types of triangles in the
figure and determine how many of each there are.
1 isosceles acute triangle, 1 equilateral
triangle, 1 scalene right triangle
Course 2
7-7 Quadrilaterals
Learn to name and identify types of
quadrilaterals.
Course 2
7-7 Quadrilaterals
Insert Lesson Title Here
Vocabulary
parallelogram
rhombus
rectangle
square
trapezoid
kite
Course 2
7-7 Quadrilaterals
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A parallelogram has two pairs of
parallel sides.
Course 2
7-7 Quadrilaterals
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A rhombus has four congruent sides.
Course 2
7-7 Quadrilaterals
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A rectangle has four right angles.
Course 2
7-7 Quadrilaterals
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A square has four congruent sides
and four right angles.
Course 2
7-7 Quadrilaterals
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A trapezoid has exactly one pair
of parallel sides.
Course 2
7-7 Quadrilaterals
Some quadrilaterals have properties that
classify them as special quadrilaterals. Here
are six major special quadrilaterals.
A kite has exactly two pairs of congruent
adjacent sides.
Course 2
7-7 Quadrilaterals
Quadrilaterals can have more than one
name because the special quadrilaterals
sometimes share properties.
Course 2
7-7 Quadrilaterals
Additional Example 1A: Identifying Types of
Quadrilaterals
Give all the names that apply to the quadrilateral.
This figure has two pairs
of parallel sides, so it is
a parallelogram.
It has four congruent
sides, so it is also a
rhombus.
Course 2
7-7 Quadrilaterals
Additional Example 1B: Identifying Types of
Quadrilaterals
Give all the names that apply to the quadrilateral.
The figure has exactly two
pairs of congruent,
adjacent sides, so it is a
kite.
It does not fit the
definitions of any of the
other special quadrilaterals.
Course 2
7-7 Quadrilaterals
Additional Example 1C: Identifying Types of
Quadrilaterals
Give all the names that apply to the quadrilateral.
The figure has two pairs of
parallel sides, so it is a
parallelogram.
It has four right angles, so
it is also a rectangle.
Course 2
7-7 Quadrilaterals
Try This: Example 1A
Give all the names that apply to the quadrilateral.
This figure has two pairs
of parallel sides, so it is
called a parallelogram.
It has four right angles,
so it is also a rectangle.
Course 2
Quadrilateral
Trapezoid
Parallelogram
Rhombus
Rectangle
Square
Kite
7-7 Quadrilaterals
Additional Example 2A: Recognizing Relationships
Between Quadrilaterals
Tell whether the statement is true or false.
Explain your answer.
A. All rhombuses are squares.
A rhombus has four congruent sides, but
some may or may not have right angles.
The statement is false.
Course 2
7-7 Quadrilaterals
Additional Example 2B: Recognizing Relationships
Between Quadrilaterals
Tell whether the statement is true or false.
Explain your answer.
B. Not all squares are rectangles.
A square has four right angles. A
rectangle also has four right angles. So a
square is a rectangle. The statement
is false.
Course 2
7-7 Quadrilaterals
Additional Example 2C: Recognizing Relationships
Between Quadrilaterals
Tell whether the statement is true or false.
Explain your answer.
C. Some parallelograms are squares.
A square has all the properties of a
parallelogram, so some parallelograms
do have equal sides and right angles;
however, some do not. The statement is
true.
Course 2
7-7 Quadrilaterals
Try This: Example 2A
Tell whether the statement is true or false.
Explain your answer.
A. All squares are rectangles.
A square has four right angles. A
rectangle also has four right angles. So a
square is a rectangle. The statement is
true.
Course 2
7-7 Quadrilaterals
Try This: Example 2B
Tell whether the statement is true or false.
Explain your answer.
B. Some rectangles are squares.
If the rectangle has four congruent
sides, then it is a square. The statement
is true.
Course 2
7-7 Quadrilaterals
Try This: Example 2C
Tell whether the statement is true or false.
Explain your answer.
C. Some trapezoids are squares.
A square has two sets of parallel sides,
but a trapezoid has only one set of
parallel sides. The statement is false.
Course 2
7-7 Quadrilaterals
Insert Lesson Title Here
Lesson Quiz: Part 1
1. Give all the names that apply to the
quadrilateral.
rhombus
quadrilateral
parallelogram
Identify the quadrilateral described.
2. 4 right angles, 4 congruent sides
square
3. only one pair of parallel sides
trapezoid
Course 2
7-7 Quadrilaterals
Insert Lesson Title Here
Lesson Quiz: Part 2
Tell if each statement is true or false. Explain.
4. All quadrilaterals are parallelograms.
False; a quadrilateral is any 4-sided polygon.
5. Every parallelogram is a rectangle.
False; a rectangle is a specific kind of parallelogram
with four right angles.
Course 2