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TRIANGLESTRIANGLES(There are three sides to
every story!)
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What kind of What kind of triangle has triangle has sidessides of…of…
4 in. , 6 in. and 3 4 in. , 6 in. and 3 in.?in.?SCALENE
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
9090oo, 70, 70oo, , 2020oo.?.? RIGHT
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What kind of What kind of triangle has triangle has sidessides of…of…
5 in. , 5 in. and 3 5 in. , 5 in. and 3 in.?in.?ISOSCELES
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
5050oo, 60, 60oo, , 7070oo.?.?ACUTE
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
6060oo, 60, 60oo, , 6060oo.?.?EQUIANGULAR
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
150150oo, 10, 10oo, , 2020oo.?.?OBTUSE
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What kind of What kind of triangle has triangle has sidessides of…of…
5 in. , 5 in. and 5 5 in. , 5 in. and 5 in.?in.?EQUILATERAL
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What kind of What kind of triangle has triangle has AnglesAngles of… of…
150150oo, 160, 160oo, , 170170oo.?.?
NO SUCH TRIANGLE
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What do we call What do we call the congruent the congruent sides of an sides of an Isosceles Isosceles Triangle?Triangle?The LEGS
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If If ABC has a ABC has a right angle at B, right angle at B, which side is the which side is the Hypotenuse?Hypotenuse?. . .A AB B BC C AC
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Which triangle is Which triangle is Impossible?Impossible?
•EQUIANGULAR OBTUSE•SCALENE ISOSCELES•RIGHT EQUILATERAL
ALL THREE!!
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Fill in the blank:Fill in the blank:
1 2 3 _____m m m
2
31
180
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:1 2 _____m m 6m
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:3 2 _____m m 4m
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:3 1 _____m m 5m
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6
5
4
2
3
1
When referring to When referring to angle 5, what do angle 5, what do we call we call ? ?
3 1and
REMOTE INTERIOR ANGLES
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6
5
4
2
3
1
Fill in the blank:Fill in the blank:4 5 6 _____m m m 360
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If this triangle is If this triangle is Equiangular:Equiangular:
1 _____m 60 2
1
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If this triangle is If this triangle is Equiangular:Equiangular:
2 _____m 120 2
1
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9x+11
12x-2
7x+3
Set up the equation needed to solve the for x:
7 3 12 1 1 01 82 9x x x 6x
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12x-19
4x-76x+8
Set up the equation needed to solve for x:
6 8 4 7 12 19x x x
10x
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80
100
100
8.7.
6.
5.4.
3.
2.1. 80
503060
40
50 30
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9.8. 7.
6. 5. 4.
3.
2.1.
110
50
50
70
60
6050130
6050
70
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2
-2C: (0, -2)
B: (1, -1)
A: (-3, 2) Find AB:
(Use distance formula or Pythagorean theorem)
2 2( 1 2) (1 3) 5
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2
-2C: (0, -2)
B: (1, -1)
A: (-3, 2) Find AC:
(Use distance formula or Pythagorean theorem)
2 2( 2 2) (0 3) 5
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2
-2C: (0, -2)
B: (1, -1)
A: (-3, 2) Find BC:
(Use distance formula or Pythagorean theorem)
2 2( 1 2) (1 0) 2 1.41
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2
-2C: (0, -2)
B: (1, -1)
A: (-3, 2) Recall:
AB=5
AC=5
BC= 1.41
What kind of triangle is it?
ISOSCELES
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A
B C
PROVE: The acute angles of a right triangle are complementary.
: .GIVEN Rt ABC
1. Given
2. Definition of Right Triangle
3. Angle Sum Theorem
4. Def. of Right Angle
5. Substitution
6.
7.
1. .Rt ABC2. .B is rt 3. 180m A m B m C
4. 90m B 95. 10 80m A m C
6. 90m A m C Subtraction Prop of Eq.
7. .A and C are compl
:PROVE A and C are complementary
Def. of Complementary
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PROVE: The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles.
4
2
31
GIVEN: The triangle pictured
PROVE: 1 2 4m m m
1. Given
2. Angle Sum Theorem
3. Supplement Theorem
4.
5.
1. The triangle pictured
2. 1 2 3 180m m m 3. 3 4 180m m 4. 1 43 32m m m m m 5. 1 2 4m m m
Substitution
Subtraction Prop. Of Eq.
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The End