Download Triangles

10. 3
Triangles
Activity
1
2
You can find the sum of the angle
measures in a triangle.
Cut a triangle from the corner of a piece of paper.
Label the corners  A,  B, and  C.
A
C
B
Tear the corners off the triangle.
A
3
B
C
Rearrange  A,  B, and  C so that they are adjacent.
Then make a conclusion about the angles of the triangle.
A
B
C
C
B
A
C
B
A
In the activity, you found that the sum of the angle measurements in
is 180º. The sum of the angle measurements in any triangle is 180º.
ABC
10. 3
EXAMPLE
Triangles
1
Finding an Angle Measure in a Triangle
Find the value of x in the triangle shown.
26º
83º
xº + 83º + 26º = 180º
x + 109 = 180
x = 71
ANSWER
xº
Sum of angle measures in a triangle is 180º.
Add 83 and 26.
Subtract 109 from each side.
The value of x is 71.
10. 3
Triangles
Interior and Exterior Angles
The three angles of any triangle are called interior angles.
The sides of a triangle can be extended to form angles outside of the triangle
that are adjacent and supplementary to the interior angles.
These angles are called exterior angles.
exterior angle
interior angles
You can use the measures of interior angles to find the measures of exterior
angles.
10. 3
EXAMPLE
Triangles
2
Finding the Measure of an Exterior Angle
Find the value of y in the figure.
55º
To find the value of y, use the fact that
adjacent interior and exterior angles of
a triangle are supplementary.
y º + 35º = 180º
y = 145
ANSWER
Definition of supplementary angles
Subtract 35 from each side.
The value of y is 145.
35º
yº
10. 3
Triangles
You can classify any triangle by the measures of its interior angles.
Classifying Triangles by Angle Measures
Acute Triangle
Right Triangle
An acute triangle A right triangle
has three acute
has one right
angles.
angle.
60º
70º
Obtuse Triangle
An obtuse triangle
has one obtuse
angle.
120º
50º
50º
40º
35º
25º
10. 3
Triangles
Congruent Sides Just as congruent angles have the same measure,
congruent sides of a triangle have the same length.
You can use special marks to indicate that two sides or two angles of a triangle
are congruent.
X
Y
Z
In the triangle above, the marks show that XY  XZ and that Y   Z.
You can classify any triangle by the lengths of its sides.
10. 3
Triangles
Classifying Triangles by Side Lengths
Equilateral
Triangle
Isosceles
Triangle
An equilateral
triangle has 3
congruent sides.
An isosceles
triangle has at
least 2 congruent
sides.
8m
9 in.
9 in.
A scalene triangle
has no congruent
sides.
5 ft
5m
9 in.
Scalene
Triangle
8m
14 ft
11 ft
10. 3
EXAMPLE
Triangles
3
Classifying a Triangle by Angle Measures
Classify the triangle formed by the plant
hanger by its angle measures.
The triangle has one right angle, so it is a
right triangle.
10. 3
EXAMPLE
Triangles
3
Classifying a Triangle by Angle Measures
Classify the triangle formed by the plant
hanger by its angle measures.
The triangle has one right angle, so it is a
right triangle.
EXAMPLE
4
Classifying a Triangle by Side Lengths
36 in.
Classify the triangle by the lengths of its
sides.
36 in.
All three sides of the triangle are congruent, so
the triangle is both isosceles and equilateral.
36 in.