4-1A Alternative Lesson

4-1A
Name
Alternative Lesson
Date
KEY TERMS
acute triangle
hypotenuse
obtuse triangle
triangle vertex
equilateral triangle
isosceles triangle
right triangle
equiangular triangle
leg
scalene triangle
A triangle is a figure formed by three line
segments that connect three noncollinear points.
A triangle is named using its vertices and a ∆
symbol. The triangle shown is ∆ABC.
C
Vertex
Side
Side
A
B
Side
Vertex
Vertex
Triangles can be classified by their sides. Notice that the sides and angles of an isosceles triangle have
special names.
B
A
Base D
Base
angles
E
C
H
Leg
F
Leg
Vertex
angle
G
∆ABC is a scalene triangle. No ∆DEF is an isosceles triangle.
two of its sides are congruent.
At least two of its sides are
congruent.
I
∆GHI is an equilateral
triangle. All of its sides are
congruent.
Triangles can be classified by their angles. Notice that the sides of a right triangle have special names.
K
R
Leg
M
J
L
N
∆JKL is an acute
triangle. All of its
angles are acute.
P
O
∆MNO is an obtuse
triangle. It has one
obtuse angle.
G
Hypotenuse
Leg
Q
∆PQR is a right
triangle. It has one
right angle.
H
I
∆GHI is an
equiangular triangle.
All of its angles have
the same measure.
EXAMPLES
Classify each triangle using both side and angle classification.
1.
L
X
2.
3.
A
B
4.
3
R
5
N
scalene
obtuse
M
W
equilateral
equiangular
© Addison-Wesley Publishing Company, Inc.
Y
C
isosceles
acute
S
4
T
scalene
right
AWSM Focus on Geometry
67
Alternative Lesson (continued)
4-1A
Name
TRY IT
Classify each triangle using both side and angle classification. First decide how many sides are
congruent. Then look at the angles.
a.
B
b.
D
E
c.
G
L
d.
H
A
C
F
I
J
K
_______________
_______________
_______________
_______________
_______________
_______________
_______________
_______________
The Triangle Angle-Sum Theorem states: The sum of the measures of the angles of a triangle is 180°.
EXAMPLE
5. Two angles of a triangle measure 18° and 76°. What is the measure of the third angle?
18° + 76° = 94°
Find the sum of the two measures given.
The sum of the two angle measures is 94°.
180° – 94° = 86°
Subtract to find the measure of the third angle.
The measure of the third angle is 86°.
TRY IT
Find the measure of ∠A in each figure.
A
e. To find the sum of the measures of the angles given, add.
________ + ________ = ________
To find the measure of ∠A, subtract.
45°
33°
180° – ________ = ________
The measure of ∠A is ________.
f.
A
g.
h.
i.
55°
A
45°
63°
100°
A
_______________
47°
_______________
68° 68°
A
_______________
_______________
Summary A triangle is named using its vertices and a ∆ symbol. It is classified by the number of
congruent sides it has and by the measures of its angles. The sum of the measures of the angles of a
triangle is 180°.
68
AWSM Focus on Geometry
© Addison-Wesley Publishing Company, Inc.

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