Students will begin by learning what the corresponding angles postulate is (video). Then students will learn what the other three corresponding angle theorems are, and see a proof of each. These include the consecutive interior angles theorem, the alternate interior angles theorem, and the alternate exterior angles theorem. Then students will practice using these theorems. Some problems will require students to determine a missing angle, or angles (video), while others will require solving a linear equation (video). Here's an easy problem: Prove adjacent interior angles in a parallelogram are supplementary. This is a direct consequence of the consecutive interior angles theorem. Here's a video detailing the proof. The fact that adjacent interior angles are supplementary in parallelograms, will be used later to prove the converse of Thales's theorem.
Next, give your students these challenges:
- Andy's Marbles by NRICH
How many squares are in this picture?
Here's the answer: There are 9 1x1 squares, 4 2x2 squares, and 1 3x3 square. Thus, there are 14 squares in total.
Conclude by leading this investigation:
ConHex (strategy game)