TRIANGLESTRIANGLES(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

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

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

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

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

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

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

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

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

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

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

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

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

NO SUCH TRIANGLE

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

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

Which triangle is Which triangle is Impossible?Impossible?

•EQUIANGULAR OBTUSE•SCALENE ISOSCELES•RIGHT EQUILATERAL

ALL THREE!!

Fill in the blank:Fill in the blank:

1 2 3 _____m m m

2

31

180

6

5

4

2

3

1

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

6

5

4

2

3

1

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

6

5

4

2

3

1

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

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

6

5

4

2

3

1

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

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

1 _____m 60 2

1

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

2 _____m 120 2

1

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

12x-19

4x-76x+8

Set up the equation needed to solve for x:

6 8 4 7 12 19x x x

10x

80

100

100

8.7.

6.

5.4.

3.

2.1. 80

503060

40

50 30

9.8. 7.

6. 5. 4.

3.

2.1.

110

50

50

70

60

6050130

6050

70

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

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

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

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

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

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.

The End