Pre-Algebra Chapter 9

Triangles
Vocabulary
• line segment
• triangle
• vertex
• acute triangle
• obtuse triangle
• right triangle
• congruent
• scalene triangle
• isosceles triangle
• equilateral triangle
• Find the missing angle measure of a triangle.
• Classify triangles by angles and by sides.
do the angles of a triangle relate to each other?
There is a relationship among the measures of the angles of a triangle.
a. Use a straightedge to draw a triangle on a piece of paper. Then cut out
the triangle and label the vertices X, Y, and Z.
b. Fold the triangle as shown so that point Z lies on side XY as shown.
Label Z as 2.
c. Fold again so point X meets the vertex of 2. Label X as 1.
d. Fold so point Y meets the vertex of 2. Label Y as 3.
Z
Z
Z
Z
X
Step 1
Y
X
2 Y
Step 2
2
Y
Step 3
Step 4
e. Make a Conjecture about the sum of the measures of 1, 2, and 3.
Explain your reasoning.
X 1
X
1
2
3
Y
ANGLE MEASURES OF A TRIANGLE A line segment is part of a line
containing two endpoints and all of the points between them. A triangle is a
figure formed by three line segments that intersect only at their endpoints.
Each pair of segments forms
an angle of the triangle.
The vertex of each angle is a
vertex of the triangle. Vertices
is the plural of vertex.
Reading Math
Line Segment
The symbol for line segment
XY is XY .
Triangles are named by the letters at their vertices. Triangle XYZ, written
XYZ, is shown.
angle
Y
vertex
X
side
Z
The sides are XY, YZ, and XZ.
The vertices are X, Y, and Z.
The angles are X, Y, and Z.
The activity above suggests the following relationship about the angles of
any triangle.
Angles of a Triangle
• Words The sum of the measures of the angles of a triangle is 180°.
• Model x˚
• Symbols x y z 180
y˚
z˚
Lesson 9-4 Triangles 453