Teaching Strategy: Use personal whiteboards or interactive “clickers” to do a spot check. Create two or three
property questions each day and begin your class with these mini-quizzes. Encourage students to create flashcards
for the properties and use them for two-column proofs.
Stress to students that the properties of congruence can only be used when given congruence(∼=), not equality(=).
This also hold true for the properties of equality; these properties are reserved for objects that are equivalent.
Have students list properties not mentioned in this lesson. Students may come up with the distributive property of
the multiplying fractions property. Students may offer notions that are incorrect – take the time to have students
learn from incorrect thoughts!
Diagrams
The best way to describe what you can and cannot assume is “Looks are deceiving.” Reiterate to students that
nothing can be assumed. The picture must literally say one thousand words using notation such as tic marks, angle
arcs, arrows, etc.
Additional Example!Use the following diagram and ask your students to list everything they can assume from the
drawing and those things that cannot be assumed. For the latter list, ask students to list additional information needed
to clarify the drawing.
Two Column Proof
Pacing:While two-column proofs will be used for the remainder of the text, this lesson should take one to two class
periods
Goal:Students are introduced to the format of a two-column proof in this lesson. The purpose of two-column proofs
is not only to prove geometric theorems. Organizing one’s thoughts in a logical manner allows students to become
better writers and debaters.
Fun Tip!Use cut outs so students can begin to visualize two column proofs. Photocopy the following proof and cut
it into sections. Shuffle the sections and place into an envelope. Give pairs of students the envelope and a sheet of
paper with the given statement, the “to prove” statement, and the column separator. Have students sort through the
rectangles and recreate the proof.
Given:ABbisectsDE;DEbisectsAB
Prove: 4 ABM∼= 4 DCM
1.2. Reasoning and Proof