Download Triangle: A triangle is the figure formed by three segments joining

Page 1 of 4
Name
Module #3:
Date
Worksheet 12b:
Triangles: Basic Terms, Angle Sum Theorem, & Classifying Triangles
View Tutorial 12b
³Objective: Be able to classify triangles according to sides and angles,
apply the theorem about the sum of the measures of the angles of a triangle,
apply the theorem about the measure of an exterior angle of a triangle.
Triangle:
A triangle is the figure formed by three segments
joining three non-collinear points.
XYZ has: three vertices: X, Y, Z
three sides: XY, XZ, YZ
three angles: ∠X, ∠Y, ∠Z
X
Y
Z
A triangle can be classified by the number of congruent sides.
Congruent: the measures are equal. The symbol used for congruent is: ≅.
A: Scalene triangle
B: Isosceles triangle
C: Equilateral triangle
no sides congruent
at least two sides congruent
all sides congruent
A
A triangle can be classified by its angles.
A: acute triangle three acute angles (less than 90°)
B: right triangle one right (90°) angle
C: obtuse triangle one obtuse angle
A
(greater than 90°)
D: equiangular triangle all angles congruent
B
B
C
C
D
Draw a triangle that satisfies the conditions stated:
If no triangle can satisfy the conditions, write not possible.
1. a right isosceles triangle 2. an acute scalene triangle 3. an equilateral equiangular triangle
Classify each triangle according to its sides or angles. (Only one answer is needed)
4. ∆ABC has angle measures 30°, 59°, 91°
5. ∆ABC has side lengths 13, 5, 12
6. ∆ABC has side lengths 6, 6, 6 2
and angle measures 45°, 45°, 90°
Copyright 2000. All rights reserved.
48
Page 2 of 4
Name
Module #3:
Date
Worksheet 12b:
Triangles: Basic Terms, Angle Sum Theorem, & Classifying Triangles
Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.
Example 1:
80°
3x°
Find the value of x. x°
Solution
x + 3x + 80 = 180
4x + 80 = 180
4x = 100
4x = 100
4
4
x = 25°
Find the value of x:
4.
x°
100°
5.
35°
6.
x°
7.
70°
30°
x=
x°
x=
x°
x°
x=
3x°
2x°
x=
Complete:
8. If ∠A ≅ ∠B ≅ ∠C,
then m∠A = m∠B =
m∠C =
A
B
10. If ∠A ≅ ∠X and
∠B ≅ ∠Y, then
∠
≅∠
9. If m∠A = 90,
then m∠B + m∠C =
C
A
Copyright 2000. All rights reserved.
Z
C
C
B
A
.
B
X
49
Y
Page 3 of 4
Name
Module #3:
Date
Worksheet 12b:
Triangles: Basic Terms, Angle Sum Theorem, & Classifying Triangles
An exterior angle is the angle formed when one side of a
triangle is extended.
The remote interior angles are the two angles of the
exterior angle
triangle not adjacent to the exterior angle.
remote
interior
angles
Exterior Angle Theorem
The measure of an exterior angle of a triangle equals the sum of the
measures of the two remote interior angles.
Example 2:
Solution
x°
Find the value of x.
120
4x = x + 120
3x = 120
x = 40
4x°
Find the value of x:
11.
12.
13.
60°
60°
x°
x=
x° 130°
50°
x°
35°
100°
x=
Copyright 2000. All rights reserved.
x=
14.
60°
x°
x=
50
Page 4 of 4
Name
Module #3:
Date
Worksheet 12b:
Triangles: Basic Terms, Angle Sum Theorem, & Classifying Triangles
Example 3:
Solution
150°
Find the values of x and y.
x°
y°
x + 150 = 180
x = 30
150 = 90 + y
60 = y
Find the values of x and y:
15.
16.
17.
18.
50°
x° y°
x°
70°
x=
35°
y=
y°
50°
x=
x°
y°
x°
y°
30°
y=
Copyright 2000. All rights reserved.
45°
x=
140°
y=
x=
y=
51