## Length

45-90 minutes

## Curriculum Standards

- CCSS.MATH.CONTENT.HSG.CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

- CCSS.MATH.CONTENT.HSG.CO.C.9

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

- CCSS.MATH.CONTENT.HSG.CO.D.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

## Materials Needed

## Vocabulary

- postulates
- theorems
- points
- lines
- non-collinear
- planes

## Instructions

- Prepare a chart in advance with the following terms:
- Label the headers as follows:
- symbol
- definition
- example
- postulates

- To activate prior knowledge, have students turn and talk about the terms on the chart. Provide student pairs the opportunity to share what they discussed. Tell students we will revisit the chart after watching the video and complete it as a class.
- Watch the video lesson Properties and Postulates of Geometric Figures as a class. Pause at 0:45.
- 5-minute quick write: Have students write for 5 minutes about what a postulate is and why postulates are important in geometric math. Divide students into small groups to discuss their answers.

- Continue watching the video. Pause at 2:23.
- Provide each group with a sheet of chart paper. Tell groups to fold the chart paper into thirds. On the top third, have students write 'points.' In this section, have students describe and illustrate examples of the postulates that describe the properties of points and non-collinear points. Provide each group the opportunity to share their information with the class.
- Continue watching the video. Pause at 3:23.
- Have students label the middle section of the chart 'lines.' Have groups illustrate and describe the postulates related to lines in this section. Provide each group the opportunity to share with the class.
- Watch the remainder of the video.
- Have student groups complete the final section of the chart paper, which they will label 'planes.' Have students illustrate and describe related postulates and share with the class. Display these charts around the class as a reference.
- Return to the chart that was presented to students at the beginning of the class period. As a class, complete the chart by creating common definitions, examples, and student-friendly definitions of each postulate.
- Use the lesson's printable worksheet to check for understanding.

## Discussion Questions

- How are postulates different from other theorems?
- Why are postulates important?
- What is the difference between a point, line, and plane?
- What are postulates that define these differences?

## Lesson Extension

- Provide students with an index card. Have each student write a question about a postulate in which the answer is either point, line, or plane. Have students write the answer on the back of the card. Divide the students into small groups. Provide each group with a stack of cards. Have students take turns asking questions to the others in the group and competing with their peers to get the most correct answers.