Download Lesson 9-3

Lesson 10-3 Triangles
Line Segment – part of a line containing two endpoints
Triangle – the union of three line segments that intersect only at their endpoints
Vertex – is the point where the line segments of a triangle intersect
The sum of the measures of the interior angles in a triangle equals 180 degrees.
Example 1 Find Angle Measures
Find the value of x in △ABC.
mA + mB + mC = 180
x + 54 + 62 = 180
x + 116 = 180
x + 116 – 116 = 180 – 116
x = 64
Write an equation.
Substitution
Simplify.
Subtract 116 from each side.
Simplify.
The measure of A is 64
Example 2 Use Ratios to Find Angle Measures
The measures of the angles of △RST are in the ratio 1:3:5. What are the measures
of the angles?
Words
The sum of the measures is 180.
Variables
Let x represent the measure of the first angle, 3x the measure of the second
angle, and 5x the measure of the third angle.
Equation
x + 3x + 5x = 180
x + 3x + 5x = 180
9x = 180
9x 180
=
9
9
x = 20
Write the equation.
Combine like terms.
Divide each side by 9.
Simplify.
Since x = 20, 3x = 3(20) or 60, and 5x = 5(20) or 100. The measures of the angles
are 20, 60, and 100.
Classifying Angles – angles can be classified by their measure
Acute – an angle with measure less than 90 degrees
Right – an angle with measure equal to 90 degrees
Obtuse – an angle with measure great than 90 degrees and less than 180 degrees
Straight – an angle with measure equal to 180 degrees
Real-World Example 3 Classify Angles
DESIGN A lightening bolt design is shown at
the right. What type of angle is L?
M
L
64
mL < 90. So, L is an acute angle.
N
Triangles are classified by their angles and their sides.
Classifying by angles: acute, right, and obtuse
Classifying by sides: scalene, isosceles, and equilateral
Example 4 Classify Triangles
Classify each triangle by its angles and by its sides.
a.
Angles:
Sides:
ABC has one obtuse angle.
ABC has no congruent sides.
The triangle is an obtuse scalene triangle.
b.
12 cm
12 cm
Angles:
Sides:
The triangle is a right isosceles triangle.
The triangle has a right angle.
The triangle has two congruent sides.