\(A’\) and \(P\) now coincide. The points coincide because that’s how we defined our translation.
Make the image Tyler describes in each step in his proof. Tyler wrote a proof that all rectangles are similar.
ARE ALL ISOSCELES TRIANGLES SIMILAR QUIZLET SOFTWARE
Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5). In subsequent activities, students will benefit from exploring and thinking about whether each statement is true before trying to prove it. Tyler’s mistake probably came from not experimenting and sketching before he began writing a proof. Mathematicians spend much of their time experimenting, wondering, guessing, sketching, and being unsure. This activity also gives the class an opportunity to discuss the proof process. Sometimes students who struggle in geometry assume that they should just know if a statement is true, and try to jump to proof before they have explored. In addition, it gives students a chance to do error analysis and provides another way to explain why not all rectangles are similar. Students should recognize many of the moves and justifications from proofs about congruence in a previous unit, and proofs about dilations earlier in this unit.
Tyler’s proof gives students a chance to see the structure of a similarity proof.
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