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Holt CA Course 1
8-4 Triangles
Warm Up
California StandardsCalifornia Standards
Lesson Presentation
PreviewPreview
Holt CA Course 1
8-4 Triangles
Warm UpSolve each equation.1. 62 + x + 37 = 180
2. x + 90 + 11 = 180
3. 2x + 18 = 180
4. 180 = 3x + 72
x = 81
x = 79
x = 81
x = 36
Holt CA Course 1
8-4 Triangles
MG3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.Also covered: Review of 6MG2.2
California Standards
Holt CA Course 1
8-4 Triangles
Vocabulary
Triangle Sum Theorem acute triangle
right triangle obtuse triangle
equilateral triangle isosceles triangle
scalene triangle
Holt CA Course 1
8-4 Triangles
An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.
Holt CA Course 1
8-4 Triangles
If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line. You can also show this in a drawing.
Holt CA Course 1
8-4 Triangles
Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown.
The three angles in the triangle can be arranged to form a straight line or 180°.
Two sides of the triangle are transversals to the parallel lines.
Holt CA Course 1
8-4 Triangles
An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.
Holt CA Course 1
8-4 Triangles
Additional Example 1: Finding Angles in Acute, Right and Obtuse Triangles
A. Find p in the acute triangle.
73° + 44° + p° = 180°
117 + p = 180
p = 63
–117 –117
Triangle Sum Theorem
Subtract 117 from both sides.
Holt CA Course 1
8-4 Triangles
Additional Example 1: Finding Angles in Acute, Right, and Obtuse Triangles
B. Find m in the obtuse triangle.
23° + 62° + m° = 180°
85 + m = 180
m = 95
–85 –85
Triangle Sum Theorem
Subtract 85 from both sides.
23
62
m
Holt CA Course 1
8-4 Triangles
Check It Out! Example 1
A. Find a in the acute triangle.
88° + 38° + a° = 180°
126 + a = 180
a = 54
–126 –126
88°
38°
a°
Triangle Sum Theorem
Subtract 126 from both sides.
Holt CA Course 1
8-4 Triangles
B. Find c in the obtuse triangle.
24° + 38° + c° = 180°
62 + c = 180
c = 118
–62 –62 c°
24°
38°
Check It Out! Example 1
Triangle Sum Theorem.
Subtract 62 from both sides.
Holt CA Course 1
8-4 TrianglesAdditional Example 2: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
62° + t° + t° = 180°62 + 2t = 180
2t = 118
–62 –62
A. Find the angle measures in the isosceles triangle.
2t = 1182 2
t = 59
Triangle Sum TheoremSimplify.Subtract 62 from both sides.
Divide both sides by 2.
The angles labeled t° measure 59°.
Holt CA Course 1
8-4 TrianglesAdditional Example 2: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
2x° + 3x° + 5x° = 180°
10x = 180
x = 18
10 10
B. Find the angle measures in the scalene triangle.
Triangle Sum Theorem
Simplify.Divide both sides by 10.
The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.
Holt CA Course 1
8-4 TrianglesCheck It Out! Example 2
39° + t° + t° = 180°39 + 2t = 180
2t = 141
–39 –39
A. Find the angle measures in the isosceles triangle.
2t = 1412 2
t = 70.5
Triangle Sum TheoremSimplify.
Subtract 39 from both sides.
Divide both sides by 2
t°t°
39°
The angles labeled t° measure 70.5°.
Holt CA Course 1
8-4 Triangles
3x° + 7x° + 10x° = 180°
20x = 180
x = 9
20 20
B. Find the angle measures in the scalene triangle.
Triangle Sum Theorem
Simplify.Divide both sides by 20.
3x° 7x°
10x°
Check It Out! Example 2
The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°.
Holt CA Course 1
8-4 Triangles
The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure.
Let x° = the first angle measure. Then 6x° =
second angle measure, and (6x°) = 3x° =
third angle measure.
12
Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions
Holt CA Course 1
8-4 Triangles
Additional Example 3 Continued
x° + 6x° + 3x° = 180°
10x = 180 10 10
x = 18
Triangle Sum Theorem
Simplify.Divide both sides by 10.
The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure.
Holt CA Course 1
8-4 Triangles
x° = 18°
6 • 18° = 108°
3 • 18° = 54°
The angles measure 18°, 108°, and 54°. The triangle is an obtuse scalene triangle.
Additional Example 3 Continued
The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible figure.
Holt CA Course 1
8-4 Triangles
x° + 3x° + x° = 180°
5x = 180 5 5
x = 36
Triangle Sum Theorem
Simplify.Divide both sides by 5.
Check It Out! Example 3 Continued
The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible figure.
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