Geometry Ch.3

Question 1

Ruler Postulate

Answer 1

Points on a line can be numbered so that a positive number measures the distance between them.

The distance of segment AB = b - a

Question 2

Coordinate

Answer 2

a number given to a point on a number line,

or a degree measure given to a ray by using a protractor

Coordinate A is 125°

Question 3

What does A-B-C mean?

Answer 3

A-B-C means that A, B, and C are three points on the same line and B is in between A and C (Ruler Postulate)

Question 4

Write an equation for A-B-C

Answer 4

Using the ruler postulate, I can conclude this Ruler Theorem: if A-B-C, the distance of segment is

AC = AB + BC

or also AC = c - a

Question 5

Protractor Postulate

Answer 5

The rays in a half rotation can be numbered from 0°-180° so that a positive number can measure the angle between the rays.

If OD-OC-OB, then ray OC is between ray OD and OB, like this:

Question 6

What do you know about an angle bisector?

Answer 6

the angles on both sides of the bisecting ray are congruent (equal)

Question 7

What do you know about the midpoint of a line segment?

Answer 7

both line segments on the sides of the midpoint are equal

A line segment only has one midpoint

Question 8

What do you know about complementary angles?

Answer 8

they add up to 90°

Question 9

What do you know about supplementary angles?

Answer 9

They add up to 180°

Question 10

What do you know about angles in a linear pair?

Answer 10

They add up to 180° and

they share one ray to make a line.

*if the angles in a linear pair are equal, then their sides are perpendicular

Question 11

What do you know about vertical angles?

Answer 11

Vertical angles are when the sides of one angle are opposite rays to the sides of the other angle.

Vertical angles are congruent (equal)

Question 12

What do you know about perpendicular lines?

Answer 12

Perpendicular lines form 90° angles (right angles)

Question 13

What can you conclude about the sides, if the angles of a linear pair are equal?

Answer 13

The lines must be perpendicular (90 + 90 = 180)

Question 14

The definition of parallel lines

Answer 14

Two lines are parallel iff they lie on the same plane and never intersect

Question 15

How can you measure ∠DOC

Answer 15

If OD-OC-OB, then ∠​DOC = ∠​DOA - ∠​COA

or ∠​DOC = d - a

Question 16

Betweenness of Points Definition

Answer 16

A point is between two other points on the same line iff its coordinate is between their coordinates.

In X-Y-Z, Y is between X and Z