Download TRIANGLES

TRIANGLES
(There are three sides to
every story!)
What kind of triangle
has sides of…
4 in. , 6 in. and 3 in.?
SCALENE
What kind of triangle
has Angles of…
o
o
o
90 , 70 , 20 .?
RIGHT
What kind of triangle
has sides of…
5 in. , 5 in. and 3 in.?
ISOSCELES
What kind of triangle
has Angles of…
o
o
o
50 , 60 , 70 .?
ACUTE
What kind of triangle
has Angles of…
o
o
o
60 , 60 , 60 .?
EQUIANGULAR
What kind of triangle
has Angles of…
o
o
o
150 , 10 , 20 .?
OBTUSE
What kind of triangle
has sides of…
5 in. , 5 in. and 5 in.?
EQUILATERAL
What kind of triangle
has Angles of…
o
o
o
150 , 160 , 170 .?
NO SUCH
TRIANGLE
What do we call the
congruent sides of an
Isosceles Triangle?
The LEGS
If D ABC has a right
angle at B, which side
is the Hypotenuse?
A. AB
B. BC
C. AC
Which triangle is Impossible?
• EQUIANGULAR OBTUSE
• SCALENE ISOSCELES
• RIGHT EQUILATERAL
ALL THREE!!
Fill in the blank:
180
m 1  m 2  m 3  _____
2
1
3
Fill in the blank:
m 6
m 1  m 2  _____
5
2
4
1
3
6
Fill in the blank:
m 4
m 3  m 2  _____
5
2
4
1
3
6
Fill in the blank:
m 5
m 3  m 1  _____
5
2
4
1
3
6
When referring to
angle 5, what do we
call 3 and 1 ?
5
REMOTE
INTERIOR
ANGLES
2
4
1
3
6
Fill in the blank:
360
m 4  m 5  m 6  _____
5
2
4
1
3
6
If this triangle is
Equiangular:
60
m 1  _____
2
1
If this triangle is
Equiangular:
2
m 2  120
_____
1
12x-2
7x+3
9x+11
Set up the equation needed to solve the for x:
7 x  3  12 x  2  9 x  11  180
x6
6x+8
12x-19
4x-7
Set up the equation
needed to solve for x:
6 x  8  4 x  7  12 x  19
x  10
7.
50
30
6.
40
100
2.
80 1.
3.
100
60
5.
4.30
80
50
8.
50 8.
1306.
50
5.
9.
70
7.
60
60 4.
50
1.
110
2.
70
50
603.
Find AB:
A: (-3, 2)
2
-5
(Use distance
formula or
Pythagorean
theorem)
5
B: (1, -1)
C: (0, -2) -2

(1  2)  (1  3)  5
-4
2
2
Find AC:
A: (-3, 2)
2
(Use distance
formula or
Pythagorean
theorem)
-5
5
B: (1, -1)
C: (0, -2) -2

(2  2)  (0  3)  5
-4
2
2
Find BC:
A: (-3, 2)
2
-5
(Use distance
formula or
Pythagorean
theorem)
5
B: (1, -1)
C: (0, -2) -2

(1  2)  (1  0)  2  1.41
2
-4
2
Recall:
A: (-3, 2)
2
AB=5
AC=5
-5
5
B: (1, -1)
C: (0, -2) -2
BC= 1.41
What kind of
triangle is it?
-4
ISOSCELES
PROVE: The acute angles of a right triangle are
complementary.
GIVEN : Rt. ABC
A
PROVE : A and
C are complementary
C
B
1. Rt. ABC
2. B is rt.
1. Given
3. m A  m B  m C  180
3. Angle Sum Theorem
4. m B  90
2. Definition of Right Triangle
4. Def. of Right Angle
5. m A  90  m C  180
5. Substitution
6. m A  m C  90
6. Subtraction Prop of Eq.
7.
A and
C are compl. 7. Def. of Complementary
PROVE: The measure of an exterior angle of a
triangle is equal to the sum of its remote interior
angles.
GIVEN: The triangle pictured
2
PROVE:
1
3
m 1 m 2  m 4
4
1. The triangle pictured
1. Given
2. m 1  m 2  m 3  180
2. Angle Sum Theorem
3. Supplement Theorem
3. m 3  m 4  180
4. m 1  m 2  m 3  m 3  m 4 4.
5. m 1  m 2  m 4
Substitution
5. Subtraction Prop. Of Eq.
The End