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PRE-QUIZ #2: TRIANGLES
1. A three-sided polygon
2. A triangle with no congruent
sides
3. A triangle with at least two
congruent sides
4. A triangle with all angles
congruent
5. The sum of the measures of the
angles in a triangle
Optical art is a
form of abstract
art that creates
special effects by
using geometric
patterns.
Definition: TRIANGLE
If A, B, and C are any three noncollinear
points, then the union of the segments AB, BC,
and AC is called a triangle, and is denoted by
ABC.
B
vertices
A
three angles
A
B
C
C
sides
AB, BC, AC
 According to its sides
scalene
triangle
no sides
congruent
 According to its sides
isosceles
triangle
at least
two sides
congruent
 According to its sides
equilateral
triangle
all sides
congruent
 According to its angles
acute
triangle
3 acute angles
 According to its angles
right
triangle
1 right angle
 According to its angles
obtuse
triangle
1 obtuse angle
 According to its angles
equiangular
triangle
3 congruent angles
4
1
3
5
2
m4 + m3 + m5 = 180
m1 + m3 + m2 = 180
Theorem:
The sum of the measures of the
angles of a triangle is 180.
3
1
2
m1 + m2 + m3 = 180
Corollary:
If two angles of one triangle are
congruent to two angles of a second
triangle, then the third angles are
congruent.
A
E
G
36
36
B
C
F
If B  G
and C  E,
then A  F.
Corollary:
Each angle of an equiangular
60
triangle measures ____.
Corollary:
In a triangle, there can be at
most one right angle, or at most
one obtuse angle.
Corollary:
The acute angles of a right
triangle are complementary.
x
(90 – x)
2
7
1
8
6
3
9
4
10
5
EXTERIOR ANGLE OF A TRIANGLE
an angle that forms a linear pair
with an angle of a triangle
2
9
4
8
1
7
3
6
10
5
REMOTE INTERIOR ANGLES
the two non-adjacent interior
angles of a triangle with respect to
its exterior angle
Theorem:
The measure of an exterior angle
of a triangle is equal to the sum of
the measures of its two remote
interior angles.
2
4
3
m5 = m2 + m3
1
5
a. scalene right triangle
b. isosceles obtuse triangle
c. isosceles acute triangle
d. equilateral right triangle
e. isosceles equiangular triangle
f. scalene acute triangle
g. scalene equiangular triangle
Find the measure of the numbered angle.
41
1
57
Find the measures of the numbered angles.
3
43
2
1
126
Find the measures of the numbered angles.
93
12
1
2
3
25
Find the measures of the numbered angles.
99
1 2
3
Find the measures of the numbered angles.
58
29
2
1
136
Find the measures of the numbered angles.
106
2
3
5
1
52
4
One of the acute angles of a
right triangle has a measure
that is five less than four
times the measure of the
other. Find the measures of
the acute angles.
The measure of an exterior
angle of a triangle is 133. The
measure of one of its remote
interior angles is forty four
less than twice the measure
of the other. What are the
measures of the remote
interior angles?
Always, Sometimes, Never
1.A triangle has three acute angles.
2.Equilateral triangles are isosceles.
3. An isosceles triangle is obtuse.
4.The measure of an
exterior angle is greater
than the sum of the
measures of its
remote interior angles.
Always, Sometimes, Never
5. In an obtuse triangle,
the acute angles are
complementary.
6. The sum of the
measures of the angles
of an acute triangle is 180.
7. An acute triangle is an
equiangular triangle.
Always, Sometimes, Never
8. An isosceles right
triangle has two acute
angles.
9. If the measure of each
angle of a triangle is 60,
then the triangle is isosceles.
10. If one of the exterior angles of a
triangle is obtuse, then its remote
interior angles are both acute.
HOMEWORK # 19
Textbook pages 98-100:
Numbers 1-4; 7-10; 13-29; 35-40
(to be checked on Monday)