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9-3 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.
9-3 Triangles
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°.
9-3 Triangles
An acute triangle has 3 acute angles. A
right triangle has 1 right angle. An obtuse
triangle has 1 obtuse angle.
9-3 Triangles
Additional Example 1A: Finding Angles in Acute,
Right, and Obtuse Triangles
Find c° in the right triangle.
9-3 Triangles
Additional Example 1B: Finding Angles in Acute,
Right, and Obtuse Triangles
Find m° in the obtuse triangle.
9-3 Triangles
Check It Out: Example 1A
Find b° in the right triangle.
38°
b°
9-3 Triangles
Check It Out: Example 1B
Find x° in the right triangle.
9-3 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.
9-3 Triangles
Additional Example 2A: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
Find the angle measures in the isosceles
triangle.
9-3 Triangles
Additional Example 2B: Finding Angles in Equilateral,
Isosceles, and Scalene Triangles
Find the angle measures in the scalene
triangle.
9-3 Triangles
Check It Out: Example 2A
Find the angle measures in the isosceles
triangle.
36°
m°
m°
9-3 Triangles
Check It Out: Example 2B
Find the angle measures in the scalene
triangle.
34p°
8p°
P°+ 8°
9-3 Triangles
Additional Example 3: 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.
9-3 Triangles
Additional Example 3 Continued
Let x° = the first angle measure. Then 6x° =
second angle measure, and 1 (6x°) = 3x° =
2
third angle.
9-3 Triangles
Check It Out: Example 3
The second angle in a triangle is twice as large
as the first. The third angle measure is the
average of the first two angle measures. Find
the angle measures and draw a possible
figure.