# Triangles

Document Sample

```					        Triangles

5.3

Pre-Algebra
Warm Up

Solve each equation.
1. 62 + x + 37 = 180 x = 81

2. x + 90 + 11 = 180   x = 79

3. x + x + 18 = 180    x = 81

4. 180 = 2x + 72 + x   x = 36
Learn to find unknown angles in
triangles.
Vocabulary

Triangle Sum Theorem
acute triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle
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.
Draw a triangle and extend one side.
Then draw a line parallel to the
extended side, as shown.
The sides of
the triangle
are
transversals to
the parallel
lines.

The three angles in the triangle can be
arranged to form a straight line or 180°.
An acute triangle has 3 acute angles. A
right triangle has 1 right angle. An obtuse
triangle has 1 obtuse angle.
Example: Finding Angles in Acute, Right
and Obtuse Triangles
Find p in the acute triangle.

73° + 44° + p = 180°

117° + p = 180°
–117°      –117°

P = 63°
Example: Finding Angles in Acute, Right,
and Obtuse Triangles
Find c in the right triangle.

42° + 90° + c = 180°

132° + c = 180°
–132°       –132°

c = 48°
Example: Finding Angles in Acute, Right,
and Obtuse Triangles
Find m in the obtuse triangle.

23° + 62° + m = 180°

85° + m = 180°
–85°        –85°

m = 95°
Try This

Find a in the acute triangle.

88° + 38° + a = 180°
38°
126° + a = 180°
–126°      –126°

a = 54°
a°    88°
Try This

Find b in the right triangle.

38°
38° + 90° + b = 180°

128° + b = 180°
–128°       –128°

b = 52°              b°
Try This

Find c in the obtuse triangle.

24° + 38° + c = 180°
38°
62° + c = 180°
24°
–62°      –62°                c°

c = 118°
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.
Example: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
Find angle measures in the equilateral triangle.

3b° = 180°    Triangle Sum Theorem

3b° 180°     Divide both
=
3    3       sides by 3.
b° = 60°

All three angles measure 60°.
Example: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
Find angle measures in the isosceles triangle.

62° + t° + t° = 180°     Triangle Sum Theorem
62° + 2t° = 180°      Combine like terms.
–62°          –62°     Subtract 62° from both sides.
2t° = 118°

2t° = 118°
Divide both sides by 2.
2     2
t° = 59°
The angles labeled t° measure 59°.
Example: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
Find angle measures in the scalene triangle.

2x° + 3x° + 5x° = 180°     Triangle Sum Theorem

10x° = 180°    Combine like terms.
10    10      Divide both sides by 10.
x = 18°
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°.
Try This
Find angle measures in the isosceles triangle.

39° + t° + t° = 180°   Triangle Sum Theorem
39° + 2t° = 180°    Combine like terms.
–39°          –39°   Subtract 39° from both sides.
2t° = 141°
2t° = 141°
Divide both sides by 2
2      2
39°
t° = 70.5°

The angles labeled t° measure 70.5°.   t°     t°
Try This
Find angle measures in the scalene triangle.

3x° + 7x° + 10x° = 180° Triangle Sum Theorem

20x° = 180° Combine like terms.
20     20 Divide both sides by 20.

x = 9°
The angle labeled 3x° measures         10x°
3(9°) = 27°, the angle labeled 7x°
measures 7(9°) = 63°, and the
angle labeled 10x° measures
10(9°) = 90°.
3x°          7x°
Try This

Find angle measures in the equilateral triangle.

3x° = 180°    Triangle Sum Theorem

3x° 180°
=
3    3                      x°
x° = 60°

All three angles measure 60°.     x°        x°
Example: Finding Angles in a Triangle that
Meets Given Conditions

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
picture.

Let x° = the first angle measure. Then 6x° =
second angle measure, and 1 (6x°) = 3x° =
2
third angle measure.
Example Continued

Let x° = the first angle measure. Then 6x° =
second angle measure, and 1 (6x°) = 3x° =
third angle.                 2

x° + 6x° + 3x° = 180°    Triangle Sum Theorem
10x° = 180°     Combine like terms.
10     10       Divide both sides by 10.
x° = 18°
Example Continued

Let x° = the first angle measure. Then 6x° =
second angle measure, and 1 (6x°) = 3x° =
third angle.                 2

x° = 18°     The angles measure 18°,
3 • 18° = 54°     54°, and 108°. The triangle
6 • 18° = 108°    is an obtuse scalene
triangle.

X° = 18°
Try This

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 picture.

Let x° = the first angle measure. Then 3x° =
second angle measure, and 1 (3x°) = x° =
3
third angle measures.
Try This Continued

Let x° = the first angle measure. Then 3x° =
second angle measure, and 1 (3x°) = 3x° =
third angle.                 3

x° + 3x° + x° = 180°     Triangle Sum Theorem
5x° = 180°     Combine like terms.
5     5       Divide both sides by 5.
x° = 36°
Try This Continued

Let x° = the first angle measure. Then 3x° =
second angle measure, and 1 (3x°) = x° =
third angle.                 3
The angles measure 36°,
x° = 36°
36°, and 108°. The triangle
3 • 36° = 108°   is an obtuse isosceles
x° = 36°    triangle.

108°

36°                  36°
Lesson Quiz: Part 1

1. Find the missing angle measure in the
acute triangle shown. 38°

2. Find the missing angle measure in the
right triangle shown. 55°
Lesson Quiz: Part 2

3. Find the missing angle measure in an acute
triangle with angle measures of 67° and 63°.
50°

4. Find the missing angle measure in an obtuse
triangle with angle measures of 10° and 15°.
155°

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 8 posted: 11/24/2011 language: English pages: 28
How are you planning on using Docstoc?