Download Lesson 10-4

Lesson 10-4 Triangles
A triangle is a polygon with three sides and three angles.
Sum of the interior angles of a triangle is 180⁰.
Example 1 Find a Missing Measure
ALGEBRA Find mC in ABC if mA = 51, mB = 103, and mC = x.
Write and solve an equation to find mC.
mA + mB + mC = 180
The sum of the measures is 180.
51 + 103 + x = 180
Write the equation.
154 + x = 180
Simplify.
– 154
– 154
Subtract 154 from each side.
x = 26
So, the measure of C is 26.
Example 2 Test EXAMPLE
Find a Missing Measure
A piece of slate tile is in the shape of a triangle. Two of the angles have measures 69
and 55. What is the measure of the third angle?
A 21
B 35
C 56
D 125
Read the Test Item
To find the missing measure, write and solve an equation.
Solve the Test Item
Let x represent the measure of the third angle.
69 + 55 + x = 180
The sum of the measures is 180.
124 + x = 180
Simplify.
– 124
– 124
Subtract 124 from each side.
x = 56
The measure of the third angle is 56. So, the answer is C.
Congruent Segments – segments that are the same length
Classifying Triangles using Angles
Acute Triangle – has all acute angles
Right Triangle – has one right angle
Obtuse Triangle – has one obtuse angle
Classifying Triangles using Sides
Scalene Triangle – no congruent sides (all different lengths)
Isosceles Triangle – two congruent sides
Equilateral Triangle – a triangle with three congruent sides
Example 3 Real-World EXAMPLE
Classify the triangle by its angles and by its sides.
The triangle has three acute angles and two congruent sides.
So, it is an acute, isosceles triangle.
Example 4 Draw Triangles
Draw a triangle with two acute angles and no congruent sides.
Then classify the triangle.
Draw an acute angle. The two
segments of the angle should
have different lengths.
Connect the two segments to
form a triangle.
The triangle is an acute scalene triangle.
Example 5 Draw Triangles
Draw a triangle with one obtuse angle and two congruent sides.
Then classify the triangle.
Draw an obtuse angle. The two
segments of the angle should
be congruent.
Connect the two segments to
form a triangle.
The triangle is an obtuse isosceles triangle.