OTCQ The Straight Angle:

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OTCQ The Straight Angle: The degree measure of a straight angle is 180 °. Given:  ABC is a straight angle and  ABD = 125 °. What can you conclude about  DBC. D. 125 °. A. B. C. OTCQ # 2 The Straight Angle:

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## OTCQ The Straight Angle:

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OTCQ

The Straight Angle:

The degree measure of a straight angle is 180°. Given:  ABC is a straight angle and  ABD = 125°.

What can you conclude about  DBC

D

125°

A

B

C

OTCQ # 2

The Straight Angle:

The degree measure of a straight angle is 180°. Given:  ABC is a straight angle and  ABD = 125°.

What can you conclude about  DBC

D

125°

55°

A

B

C

OTCQ # 2

The Straight Angle:

The degree measure of a straight angle is 180°. Given:  ABC is a straight angle and  ABD = 125°.

What can you conclude about  DBC

D

125°

55°

A

B

C

VERTEX IS THE MIDDLE LETTER

### AIM 4-2

How do we use definitions and postulates in proofs?

GRP 7, GPS 2 and GPS 4

Homework: See HWK Sheet

### OBJECTIVE

1. SWBAT explain and use properties and postulates in proofs.

Properties of Equality

1) Reflexive: a = a

2) Symmetric: If a = b then b = a.

• Transitive:

If a = b and b = c, then a = c.

• Substitution:

If a = b, then a can be replaced by b.

Postulates 1-4
• 1. A straight line segment can be drawn joining any two points.
• 2. Any straight line segment can be extended indefinitely in a straight line.
• 3. Two lines cannot intersect in more than one point.
• 4. One and only one circle can be drawn with any given point as center and the length of any given line segment as the radius.
Postulates 5 -8
• 5. At any given point on a given line, one and only one perpendicular line can be drawn to the line.
• 6. From a given point not on a given line, one and only one perpendicular can be drawn to the given line.
• 7. For any two distinct points, there is only one positive real number that is the distance between the two points.
• 8. The shortest distance between two points is the length of the line segment joining these two points.
Postulates 9- 10
• 9. A line segment has one and only one midpoint.
• 10. An angle has one and only one bisector.
Proof practice:

given: ABC is a straight angle and BD bisects ABC.

Prove BD AC

Statements

Reasons

D

given: ABC is a straight angle and BD bisects ABC.

Prove BD AC

A

C

B

Statements

Reasons

1.  ABC is a straight angle

and BD bisects ABC

Conclusion: BD AC

1. Given

D

given: ABC is a straight angle and BD bisects ABC.

Prove BD AC

A

C

B

Statements

Reasons

1.  ABC is a straight angle

and BD bisects ABC.

2.If  ABC is a straight ○

Angle, then m ABC is 180.

Conclusion: BD AC

1. Given

2. Straight angle definition.

D

given: ABC is a straight angle and BD bisects ABC.

Prove BD AC

A

C

B

Statements

Reasons

• 1.  ABC is a straight angle
• and BD bisects ABC.
• 2.If  ABC is a straight
• Angle, then m ABC is
• 180° .
• If BD bisects a 180° angle,
• then each resulting angle
• will equal 90° .
• Conclusion: BD AC

1. Given

2. Straight angle postulate.

3. Angle Bisector postulate.

D

given: ABC is a straight angle and BD bisects ABC.

Prove BD AC

A

C

B

Statements

Reasons

1. Given

2. Straight angle postulate.

3. Angle Bisector postulate.

4. Perpendicular lines definition.

• 1.  ABC is a straight angle
• and BD bisects ABC.
• 2.If  ABC is a straight
• Angle, then m ABC is
• 180° .
• If BD bisects a 180° angle,
• then each resulting angle
• will equal 90° .
• 4. Lines that intersect at a 90°
• Angle are perpendicular.
• Conclusion: BD AC

4

1

2

3

Statements

Reasons

Given: The Diagram Prove: 1  3 + 4

Geometry Test Sample on Postulates Name:_________________Nelson Mandela High School Maximum Value 35: Score =

Part 1 Vocabulary: Fill in the missing words in each postulate exactly as presented in class and in Section 4-1. 1 point each. Write clearly. No partial credit.

• Two lines cannot _________________________________________________

____________________________________________________________________

2. One and only one circle can be drawn with

____________________________________________________________________

____________________________________________________________________

3. From a given point not on a given line,

____________________________________________________________________

____________________________________________________________________

4. The shortest distance between two points is ________________________________

____________________________________________________________________.

5. A line segment has one _______________________________________________.