Geometry Chapter 2.3

1. Geometry Chapter 2.3 SEGMENT AND ANGLE RELATIONSHIPS

2. Definition of congruence Congruent segments Definition of a Segment bisector Definition of Midpoint Distance formula Congruent angles Angle bisector Perpendicular to a line Perpendicular to a plane Goal 1: Building Your Geometric Vocabulary

3. Definition of congruence If two objects have the exact same shape (are line segments, rays, lines, angles, triangles, polygons, etc.) and they have the exact same measurement (distance, angle measure, etc.) then they are congruent. 

4. Definition of congruence Definitions can be interpreted both ways (forward or backward), in other words if two segments have the same measure, then they are congruent AND if two segments are congruent, then they have the same measure.

5. Congruent segments Two segments that are congruent have the same length. We mare congruent segments with “tic” marks.

6. Congruent Segments mean equal length If two segments are congruent, then they have the same measure. Because of the definition of congruence.

7. Congruent angles Congruent angles have the same measure. We mark their equal angles by using the same number of arcs. (Please place an arc on each of the angles drawn below.) If two angles are congruent, then they have the same measure. Because of the definition of congruence.

8. Segment bisector A segment bisector is any point, line, line segment, ray, or plane that intersects a line segment to create two smaller line segments that have equal length. is a ray that cuts into two congruent segments and Therefore, is a segment bisector.

9. Angle Bisector An angle bisector is any line, line segment, ray, or plane that intersects an angle at its vertex to create two smaller angles that have equal measurements. Ray BD bisects ABC. Ray BD is called an angle bisector.

10. Definition of Midpoint The midpoint of a segment is the point that divides the segment into two congruent segments. Midpoint formula If C is the midpoint of segment AB, then AB = CB.

11. Definition of perpendicular Two lines are perpendicular if they intersect to form a right angle. A line is perpendicular to a plane if it is perpendicular to each line in the plane that intersects it.

12. Distance Formula The distance between two points A(xA,yA) and B(xB,yB) is