**Objectives**

- Apply knowledge of points, lines, and distance along a line to create precise definitions for an angle and line segment.
- Use dimensions to precisely describe points, line segments, rays, lines, and angles.
- Identify acute, obtuse, and right angles when given angle measures or diagrams.
- Identify linear, supplementary, and complementary angle pairs in diagrams.
- Define and apply congruence to segment midpoints and angle bisectors.
- Use precise notation to distinguish between a line segment and its measure, and between congruent and equal figures.

**Key Terms**

- Acute Angle – an angle that measures less than 90°. An acute angle is smaller than a right angle.
- Adjacent Angles – angles that share a vertex and one side.
- Angle – the object formed by two rays that share the same endpoint.
- Angle Addition Postulate – if point C lies in the interior of AVB, then
*m*AVC +*m*CVB =*m*AVB. - Angle Bisector – a ray that divides an angle into two angles of equal measure.
- Complementary – having angle measures that add up to 90°. If two complementary angles are adjacent, they form a right angle.

- Congruent – having the same size and shape. If polygons are congruent, their corresponding sides and angles are also congruent. The symbol means “congruent.”
- Endpoint – a point at the end of a ray, either end of a line segment, or either end of an arc.
- Linear Pair – a pair of adjacent angles whose measures add up to 180°. Linear pairs of angles are supplementary.
- Line – the set of all points in a plane that are equidistant from two points.
- Line Segment – a part of a line with endpoints at both ends. The symbol AB means “the line segment with endpoints A and B.” It is sometimes called a segment.
- Midpoint – the point halfway between the endpoints of a line segment.
- Point – the most basic object in geometry, used to mark and represent locations. Points have no length, width, or height.
- Obtuse Angle – an angle with a measure greater than 90° but less than 180°.
- Ray – a part of a line that starts at an endpoint and extends forever in one direction. The symbol means “the ray with endpoint A that passes through B.”
- Right Angle – an angle that measures 90°. Right angles are often marked with a small square symbol. Perpendicular lines form right angles.
- Segment Addition Postulate – a postulate stating that if AC + BC = AB, then point C is between points A and B.
- Straight Angle – an angle whose sides form a line. The measure of a straight angle is 180°.
- Supplementary – having angle measures that add up to 180°. If two supplementary angles are adjacent, they form a straight angle.
- Vertex – a point at which rays or line segments meet to form an angle. The plural of vertexis vertices. The vertices of a polygon are the points at which the sides meet. The vertices of a polyhedron are the points at which at least three edges meet.
- Zero Angle – an angle that has a measure of zero degrees and whose sides overlap to form a ray.

Notes

- Segment Notation can be written 3 different ways
- 1. Segment Notation (Sentence): The
**length**of is 3 inches.- The word
**length**(above) is required for to have a bar on top of the letters.

- The word
- 2. Length Notation (Sentence): AB is 3 inches.
- 3. Length Notation (Equation): AB = 3 inches.

- 1. Segment Notation (Sentence): The

- Angle Notation

1. Use the vertex only

2. Use the vertex and two other points (vertex is in the middle)

3. Use the number assigned to the angle

- A protractor is used to measure angles in degrees (Apex Pg 12).
- To measure an angle with a protractor, follow these steps:
- Step 1: Position the protractor’s red circle over the angle’s vertex.
- Step 2: Align the “0” mark with one of the angle’s sides.
- Step 3: See where the other side of the angle falls on the protractor.
- This shows the difference between the rays’ directions, which is the angle’s measure.

- To measure an angle with a protractor, follow these steps:

- Angle Measures
- A
**zero**angle is a ray and measures 0°. - A
**straight**angle is a straight line and measures 180°. - A
**right**angle measures 90°. - An
**acute**angle measures less than 90°. - An
**obtuse**angle measures more than 90°.

- A

means “the**m**∠AVM**measure**” of ∠*AVM*- The
**angle addition postulate**states that if a point C is inside ∠AVB, then m∠AVC + m∠CVB = m∠AVB

**Congruent angles**have the same angle measure