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TRIANGLES (There are three sides to every story!).

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TRIANGLES TRIANGLES (There are three sides to every story!)
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Page 1: TRIANGLES (There are three sides to every story!).

TRIANGLESTRIANGLES(There are three sides to

every story!)

Page 2: TRIANGLES (There are three sides to every story!).

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

Page 3: TRIANGLES (There are three sides to every story!).

What kind of What kind of triangle has triangle has AnglesAngles of… of…

9090oo, 70, 70oo, , 2020oo.?.? RIGHT

Page 4: TRIANGLES (There are three sides to every story!).

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

Page 5: TRIANGLES (There are three sides to every story!).

What kind of What kind of triangle has triangle has AnglesAngles of… of…

5050oo, 60, 60oo, , 7070oo.?.?ACUTE

Page 6: TRIANGLES (There are three sides to every story!).

What kind of What kind of triangle has triangle has AnglesAngles of… of…

6060oo, 60, 60oo, , 6060oo.?.?EQUIANGULAR

Page 7: TRIANGLES (There are three sides to every story!).

What kind of What kind of triangle has triangle has AnglesAngles of… of…

150150oo, 10, 10oo, , 2020oo.?.?OBTUSE

Page 8: TRIANGLES (There are three sides to every story!).

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

Page 9: TRIANGLES (There are three sides to every story!).

What kind of What kind of triangle has triangle has AnglesAngles of… of…

150150oo, 160, 160oo, , 170170oo.?.?

NO SUCH TRIANGLE

Page 10: TRIANGLES (There are three sides to every story!).

What do we call What do we call the congruent the congruent sides of an sides of an Isosceles Isosceles Triangle?Triangle?The LEGS

Page 11: TRIANGLES (There are three sides to every story!).

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

Page 12: TRIANGLES (There are three sides to every story!).

Which triangle is Which triangle is Impossible?Impossible?

•EQUIANGULAR OBTUSE•SCALENE ISOSCELES•RIGHT EQUILATERAL

ALL THREE!!

Page 13: TRIANGLES (There are three sides to every story!).

Fill in the blank:Fill in the blank:

1 2 3 _____m m m

2

31

180

Page 14: TRIANGLES (There are three sides to every story!).

6

5

4

2

3

1

Fill in the blank:Fill in the blank:1 2 _____m m 6m

Page 15: TRIANGLES (There are three sides to every story!).

6

5

4

2

3

1

Fill in the blank:Fill in the blank:3 2 _____m m 4m

Page 16: TRIANGLES (There are three sides to every story!).

6

5

4

2

3

1

Fill in the blank:Fill in the blank:3 1 _____m m 5m

Page 17: TRIANGLES (There are three sides to every story!).

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

Page 18: TRIANGLES (There are three sides to every story!).

6

5

4

2

3

1

Fill in the blank:Fill in the blank:4 5 6 _____m m m 360

Page 19: TRIANGLES (There are three sides to every story!).

If this triangle is If this triangle is Equiangular:Equiangular:

1 _____m 60 2

1

Page 20: TRIANGLES (There are three sides to every story!).

If this triangle is If this triangle is Equiangular:Equiangular:

2 _____m 120 2

1

Page 21: TRIANGLES (There are three sides to every story!).

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

Page 22: TRIANGLES (There are three sides to every story!).

12x-19

4x-76x+8

Set up the equation needed to solve for x:

6 8 4 7 12 19x x x

10x

Page 23: TRIANGLES (There are three sides to every story!).

80

100

100

8.7.

6.

5.4.

3.

2.1. 80

503060

40

50 30

Page 24: TRIANGLES (There are three sides to every story!).

9.8. 7.

6. 5. 4.

3.

2.1.

110

50

50

70

60

6050130

6050

70

Page 25: TRIANGLES (There are three sides to every story!).

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

Page 26: TRIANGLES (There are three sides to every story!).

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

Page 27: TRIANGLES (There are three sides to every story!).

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

Page 28: TRIANGLES (There are three sides to every story!).

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

Page 29: TRIANGLES (There are three sides to every story!).

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

Page 30: TRIANGLES (There are three sides to every story!).

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.

Page 31: TRIANGLES (There are three sides to every story!).

The End


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