Download Equilateral Triangle

A polygon is a closed figure formed by three or more
line segments that do not cross. A triangle is a
polygon with three sides. The sum of the measures
of a triangle is 180°.
Example:
80°
30°
70°
There are two ways to classify triangles:
By the number of congruent sides they have or by
their angle measures.
Classifying Triangles by Sides
Some types of triangles are shown below.
Type
Scalene triangle
A scalene triangle is a
triangle with no
Example
Properties
•No angles are congruent
•No sides are congruent
congruent sides.
Isosceles triangle
An isosceles triangle is
a triangle with at least
two congruent sides.
*at least two congruent sides
*the angles opposite
congruent sides have equal
measure. Therefore, two
angles, called base angles,
are congruent
Equilateral Triangle
An equilateral triangle
is a triangle with three
congruent sides.
•All sides are congruent
•The angles opposite
congruent sides have equal
measures, Therefore, all
angles are congruent.
Example: Classify the triangle by its sides.
The triangle has two sides that are congruent, so the
Isosceles triangle
triangle is an____________________.
Example 1
An equilateral triangle has one side with length 10
inches. What are the lengths of the other two sides?
An equilateral triangle is a triangle with three
congruent side, therefore, the length of the other two
10 inches
sides are also_______________.
Quick Check 1
1a
Classify the triangle by its sides.
scalene
1b
An equilateral triangle has one side with
length 8 m. What are the lengths of the other
two sides?
8 m
Classifying Triangles by Angles
Some types of triangles are shown below.
Type
Example
Properties
Right Triangle
A right triangle is a
triangle with one right
angle
* Exactly on angle is a right
Acute triangle
A triangle with three acute
angles
*all angles are acute
angles
Obtuse triangle
A triangle with one obtuse
angle
* Exactly one angle is an
obtuse angles. The other
two angles are acute
Equiangular triangle
A triangle with three
congruent angles
*all angles are acute
*all angles are congruent
*the sides opposite
congruent angles have equal
lengths. Therefore, all sides
are congruent.
angle. The other two angles
are acute. The acute angles
are complementary
Example: Classify the triangle by its angle measures.
38°
52°
The triangle has a right angle, so the triangle is a
right triangle
___________________________.
Example 2
A triangle has two angles that measure 60°. What is
the measure of the third angle? What is the
classification of triangle by its angle measures?
The sum of all the measures of the angles of a triangle
is 180°. We can use an equation to find the measure
of the third angle.
Let x = the measure of the third angle.
X + 60° + 60° = 180°
X + 120° = 180°
X = 60°
Since the triangle has three angles that are
congruent, the triangle is an
equiangular triangle
____________________.
Quick Check 2
2a
Classify the triangle by its angle measures.
62°
46°
2b
Acute triangle
72°
A triangle has two angles that measure 48°
and 37°. What is the measure of the third
angle? What is the classification of the
triangle by its angle measures?
48 + 37 = 85
180 – 85 = 95
48
37
95
Obtuse triangle
Using Properties to Classify Quadrilaterals.
A quadrilateral is a polygon with four sides. The sum
of the measures of the angles of a quadrilateral
is_____________________.
360°
70°
Example:
100°
80°
110°
Quadrilaterals can be classified based on the
information about their sides and angles. Some types
of quadrilaterals are shown below.
Type
Example
Properties
Parallelogram
A parallelogram is a
quadrilateral with two
pairs of parallel sides.
*opposite sides are
parallel
*opposite sides are
congruent
Rectangle
A rectangle is a
parallelogram with four
right angles.
*a rectangle has all the
Rhombus
A rhombus is a
parallelogram with four
congruent sides
*a rhombus has all the
properties of a
parallelogram
*all sides are congruent
properties of a
parallelogram
*all angles are right
angles
*adjacent sides form right
angles
Type
Example
Properties
Square
A square is a
parallelogram with
four right angles and
four congruent angles
•A square has all the
properties of a
parallelogram
•*a square has all the
properties of a
rectangle
•*a square has all the
properties of a
rhombus
Trapezoid
A trapezoid is a
quadrilateral with
exactly one pair of
parallel sides.
*exactly one pair of
opposite sides is
parallel
pentagon 5 sides
octagon
8 sides
hexagon 6 sides
decagon 10 sides
regular polygon Sides and angles
are congruent
example
regular
pentagon
irregular
pentagon
List all the triangles pictured below that fit each description.
1. Isosceles triangle_______________
2. Equilateral triangle______________
3. Scalene triangle________________
4. Acute triangle__________________
5. Obtuse triangle_________________
6. Right isosceles triangle___________
M
J
L
D
N
K
O
E
A
H
G
I
C
B
F
Circle all the names that are true for each figure.
7.
Hexagon
Quadrilateral
Octagon
polygon
Circle all the names that are true for each figure.
8.
rhombus
parallelogram
quadrilateral
Regular polygon
Circle all the names that are true for each figure.
9.
pentagon
hexagon
Octagon
polygon
Circle all the names that are true for each figure.
10.
quadrilateral
parallelogram
square
rectangle
Draw a figure to fit each description.
11. An obtuse scalene triangle
Draw a figure to fit each description.
12. An isosceles trapezoid
Draw a figure to fit each description.
13. A quadrilateral that is not a square but has all sides equal
Draw a figure to fit each description.
14. A regular hexagon
15. Can an equilateral triangle be a right triangle? Explain.
Triangles
Quadrilaterals
1
1
2
2
3
3
4
4
5
5
6
6
HOMEWORK
1. A triangle has two angles that measure 45° and
55°. What is the measure of the third angle?
A
80°
B
180°
C
90°
D
55°
HOMEWORK
2. Which of the following names could NOT describe
a triangle with two congruent sides?
F
Isosceles triangle
G
Scalene triangle
H
Right triangle
J
Acute triangle
HOMEWORK
3. Which of the following triangles best describes the
triangle with the given measures?
5
3
4
A
Right scalene triangle
B
Acute equilateral triangle
C
Obtuse equilateral triangle
D
Right Isosceles triangle
HOMEWORK
4. Which statement is always true about an isosceles
triangle?
F
It has 3 congruent angles
G
It has at least 2 congruent sides
H
It has 3 congruent sides
J
It has no congruent sides
HOMEWORK
5. Mr. Richardson bought a new triangular sail for his
sailboat. Which of the following triangles best
describes the triangular sail with the given
measures?
50°
A
obtuse isosceles triangles
B
right scalene triangle
C
acute equilateral triangle
D
Acute isosceles triangle
HOMEWORK
6. Which statement is NOT true about an equiangular
triangle?
F
The sum of the measures of the 3 angles is 180°
G
It has exactly 2 congruent angles
H
It has 3 congruent angles
J
It has 3 congruent sides
HOMEWORK
1. A diamond is cut to the following shape. Which of
the following best describes the quadrilateral with
the given measurements?
A
square
B
rhombus
C
kite
D
parallelogram
HOMEWORK
2. The profile of a tent is shown below. Which of the
following best describes the triangle with the given
measurements?
7 ft
F
right isosceles
G
acute isosceles
H
obtuse isosceles
J
acute equilateral
7 ft
43°
43°
10 ft
HOMEWORK
3. A rearview mirror on a new car is shaped as shown
below. Which of the following best describes the
quadrilateral with the given measurements?
130°
500°
A
rectangle
B
square
C
rhombus
D
trapezoid
HOMEWORK
4. A jet plane’s wing is shown below. Which of the
following best describes the triangle as shown?
F
right isosceles
G
right scalene
H
acute isosceles
J
acute scalene
56°
C
110°
50°
mABC =
mC =
A
B
HOMEWORK
1. Which statement is always true about an isosceles
triangle?
A
It has 3 congruent angles
B
It has 1 right angle
C
It has 2 congruent angles
D
It has exactly 1 acute angle
HOMEWORK
2. Which statement is always true about a pentagon?
A
It has 5 congruent angles
B
It has 5 obtuse angles
C
The sum of all the angles is 540
D
It has exactly 6 sides
HOMEWORK
3. Which statement is always true about a
quadrilateral?
A
It has exactly 4 congruent angles
B
It has 1 right angle
C
The sum of all the angles is 360
D
It has exactly 1 acute angle
HOMEWORK
4. Which statement is always true about a right
triangle?
A
It has exactly 3 congruent angles
B
It has 1 right angle
C
It has exactly 2 congruent sides
D
It has 2 obtuse angles
Friday, January 12
NO WARM UP
Get out your
homework!
HOMEWORK
1. Which of the following statements is always true
about quadrilaterals?
A
All sides are congruent
B
All angles are congruent
C
The sum of the measures of the angles is 360°
D
opposite sides are parallel
HOMEWORK
2. Which of the following statements is always true?
F
A trapezoid is a parallelogram
G
A square is a rectangle
H
A rectangle is a square
J
A quadrilateral is a parallelogram
HOMEWORK
3. Which of the following statements is NOT a name
for the figure?
4
10
A
parallelogram
B
quadrilateral
C
rectangle
D
rhombus
HOMEWORK
4. How many parallel lines does a trapeziod have?
F
1
G
3
H
3
J
4
HOMEWORK
5. How many congruent sides does a rhombus have?
A
1
B
3
C
3
D
4
HOMEWORK
6. Which of the following names is the best name for
the quadrilateral?
5
5
F
rectangle
G
rhombus
H
parallelogram
J
square
HOMEWORK
1. A triangle is a
________________
with three sides.
HOMEWORK
2. A polygon with
four sides is a
_________________
HOMEWORK
3.A polygon with five
sides is a
HOMEWORK
4. A hexagon is a
polygon with six
sides and six
HOMEWORK
5. A polygon with
eight sides is an
HOMEWORK
6. A polygon with ten
sides is a
HOMEWORK
7. A triangle with no
congruent sides is a
________________
triangle.
HOMEWORK
8. A triangle (or
trapezoid) with two
congruent sides is
HOMEWORK
9. A polygon with all
sides congruent is
HOMEWORK
10. A triangle with
a 90° angle is a
______________
triangle
HOMEWORK
11. A quadrilateral
whose opposite
sides are parallel is
a
HOMEWORK
12. A parallelogram
with four right
angles is a
HOMEWORK
13. A quadrilateral
with one pair of
parallel sides is a
HOMEWORK
14. A parallelogram
which is equilateral
is a
HOMEWORK
15. A rectangle
which is equilateral
is a