- Be sure that the students have a current list of postulates, properties and vocabulary where they can access it
easily. - Here are some helpful hints for students in working on two- column proofs.
a. Draw a diagram to better understand the vocabulary in the given. For example, if you are working on proving
that points are collinear, then draw a diagram of the collinear points. Then look at what statements and reasons
you can write about it.
b. Look at the vocabulary in the given. Example 2 has the word “bisects” in it. Therefore, you will need a
statement and reason that explains bisects.Example 2 also has a congruent symbol in it. Therefore, you will need a statement and a reason that addresses
congruency.
IV.AlternativeAssessment
- Give a homework assignment where students write their own two- column proof based on a common given.
- The next day review the assignment and answers with the students. In small groups, have them write one
“best” proof for the given.
Segment and Angle Congruence Theorems
I.SectionObjectives
- Understand basic congruence properties.
- Prove theorems about congruence.
II.MultipleIntelligences
- The best way to address different learning styles in this lesson is to use diagrams and to teach this lesson as a
class discussion. - The students will need to break down the concepts provided to gain an excellent understanding of the material.
- Prior to teaching the lesson, write the intention on the board or overhead. This will assist all visual learners
and help special needs students too. - “To prove congruence properties, we turn congruence statements into number statements, and use properties
of equality. - Here are some steps to write on the board:
a. Take the given and notice whether you are working with segments or angles.
b. Think of converting to measurement. For exampleAB∼=AB, as a statement, we can say thatAB=AB. We are
working with the measurement or length of the segment here. We have changed this to numbers. With angles,
change to show the measurement of the angles is equal.III.SpecialNeeds/Modifications
- Be sure that students have a page of notes out that explain the properties of equality.
- Review each of the properties and what each means.
- Show students how to draw a diagram to illustrate a given statement. A picture often helps special needs
students. - Explain that postulates don’t need to be proven.
Chapter 4. Geometry TE - Differentiated Instruction