Lazy Mathematicians A Lesson from NCTMs Triangle Congruence ARC - PowerPoint PPT Presentation

Jul 05, 2023 •280 likes •382 views

Lazy Mathematicians A Lesson from NCTMs Triangle Congruence ARC Warm-Up Given: ABE, ABC, and BCD are equilateral. Question: Do triangles ABE and BCD have to be congruent? How do you know? Challenge 1 Challenge: Name

Lazy Mathematicians A Lesson from NCTM’s Triangle Congruence ARC
Warm-Up Given: 𝝚 ABE, 𝝚 ABC, and 𝝚 BCD are equilateral. Question: Do triangles 𝝚 ABE and 𝝚 BCD have to be congruent? How do you know?
Challenge 1 Challenge: Name as many pairs of objects that must be congruent as you can.
Challenge 2 Given that BC, BL, and BD are radii of the same circle, and BL bisects angle DBC, name as many pairs of congruent objects as you can.
Making Connections: What Information Did We Know in Both Cases?
Conjectures about Triangle Congruence If all three pairs of corresponding sides are congruent, then the triangles must be congruent
Testing Our Conjectures NCTM Illuminations App
Which Conditions Seem to Guarantee Congruence? Side-Side-Side
Which Conditions Definitely Don’t Guarantee Congruence?
Reflections/Summary “Right now, I can show triangles are congruent by _____________________________ OR 1. _____________________________. For me, right now, _____________________________ is the easier method because _____________________________. I can image that if a problem were like _____________________________, it might be easier to do the other method.” 1. Patrick says that if you have two triangles and you know any two pairs of corresponding sides are congruent and any pair of corresponding angles are congruent, then the triangles have to be congruent. Sponge Bob says he doesn’t think that’s true but he’s having a hard time explaining just when it is true. Please help Sponge Bob, using what you explored today. 1. Agree or Disagree: Looking at examples in the app proves that these shortcut sets of conditions guarantee triangle congruence. Why do you agree or disagree?

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