WARM UP

Snap Wink O 1. Stand up. O 2. Wink your left eye and snap your right hand index finger and thumb at the same time. O 3. Wink your right eye and snap your left hand index finger and thumb at the same time. O 4. Switch back and forth as fast as you can.

Chapter 1 Honors Geometry 1-1 Points, Lines and Planes

Collinear Points: Points that lie on the same line. Coplanar Points: points that lie on the same plane.

Example 1A: Use the figure to name a line containing point K

Answer: The line can be named as line a. There are three points on the line. Any two of the points can be used to name the line For example:

Example 1B: Use the figure to name a plane containing point L

Answer: The plane can be named as plane B You can also use any three NONCOLLINEAR points to name the plane. For example: plane JKM plane KLM plane JLM

The letters of each of these names can be reordered to create other acceptable names for this plane. For example, JKM can also be written as JMK, MKJ, KJM, KMJ, and MJK. There are 15 different three-letter names for this plane.

Example 2A: Name the geometric shape modeled by a 10 x 12 patio.

Answer: The patio models a plane

Example 3: Name the geometric shape modeled by a button on a table

Answer: The button on the table models a point on a plane.

Two or more geometric figures intersect if they have one or more points in common The intersection of the figures is the set of points the figures have in common.

Example 4 Draw and label a figure for the following situation: Plane R contains lines AB and DE, which intersect at point P. Add point C on plane R so that it is not collinear with line AB or line DE. Draw a surface to represent plane R and label it.

Your plane should look something like this:

Example 5: Draw and label a figure for the following situation. Line QR on a coordinate plane contains Q(-2, 4) and R(4, -4). Add point T so that T is collinear with these points

Example 5: Draw and label a figure for the following situation. Line QR on a coordinate plane contains Q(-2, 4) and R(4, -4). Add point T so that T is collinear with these points

Example 6 A: How many planes appear in this figure?

Example 6 A: How many planes appear in this figure? There are 2 planes, plane S and plane ABC

Example 6 B: Name three points that are collinear.

Example 6 B: Name three points that are collinear. Answer: Points A, B, and D are collinear

Example 6 C. Are points A, B, C, and D coplanar? Explain.

Example 6 C. Are points A, B, C, and D coplanar? Explain. Answer: Points A, B, C, and D all lie in plane ABC, so they are coplanar.

Example 6 D: At what point do lines DB and CA intersect?

Example 6 D: At what point do lines DB and CA intersect? The two lines intersect at point A.