Section 3-3Parallel Lines and the Triangle Angle-Sum Theorem

Activity #1

1

2 3

123

1

2 3

180321 mm

!Behold

Activity #2 180321 mm

!Behold

1

1

2

2

3

3

Formal Proof 18054m1m:Prove

ΔABC:Given

1

A

BC4 5

2 3D E

Statements Reasons

ABC 1. Given 1.

on)constructi (by

postulate line Parallel 2.BC || DE 2.

angle straight a is DAE 3. diagram from Assumed 3.

DAEm3m2m1m 4. postulate addition Angle 4.

180DAEm 5. straight Def. 5.

1803m2m1m 6. onSubstituti 6.

5m3m 4m2m 8. ;

53 42 7. ; s int. alt.lines || 7.

Def. 8.

1805m4m1m 9.onSubstituti 9.

Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180˚.

Formal Proof 4m3m2m:Prove

ΔABC:Given

2

A

BC1 3

Statements Reasons

ABC 1. Given 1.

theorem sum-angle Triangle 2.

angle straight a is DCB 3. diagram from Assumed 3.

DCBm4m1m 4. postulate addition Angle 4.

180DCBm 5. straight Def. 5.

1803m2m1m 2.

onSubstituti 6.

onSubstituti 7.

Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

D 4

1804m1m 6.

4m1m3m2m1m 7.

4m3m2m 8. POE nSubtractio 8.

Classifying Triangles

Classify by Angles

60˚ 60˚

60˚

Equiangular

Acute Right Obtuse

Classify by Sides

Equilateral

Isosceles Scalene

Example 1

67˚ 48˚

x

Example 2

x

z

y

70˚

Example 3:classify by angles and sides

2

4

120˚

5

Example 4:

125˚

X

Example 5:

A triangle with a 90˚ angle has sides that are 3 cm, 4 cm, and 5 cm long. Classify the triangle by its angles and sides.

Example 6:

70˚ 42˚

y

Example 7:

90˚

76˚ x

Example 8:

2x + 28

32˚4x

Example 9:

5x + 40

10x 3x − 4

Example 10:

x

160˚125˚