Thursday, October 2, 2014

A Triangle Classic -- So many congruent parts but not enough...

Twitter Problem 10-2-14

∆ABC: AC=6,BC=9,AB=4
∆DEF: DE=6,DF=9
If angle BAC is congruent to angle EDF, EF=?


1. Not that easy to find examples where two NONCONGRUENT triangles have 5 pairs of congruent parts!

2. This might drive home the meaning of important terms like corresponding parts, included vs non-included angles, etc

3. I used this example in the classroom to help students avoid jumping to conclusions! Geometry teachers love the play on words with "ASS-U-ME" but this example may be more about SSA and its reversal!

4. SAS is both a congruence and a similarity theorem/postulate. Once the student draws the diagram and labels corresponding parts carefully the similarity should become clearer. But do you think some students would match up the congruent sides before looking for proportional parts? Let me know if you use this at some point.

5. You might challenge your students to devise other pairs of similar triangles that have 2 pairs of congruent sides and three pairs of congruent angles. Maybe they'll notice the 2:3 ratio *within* each triangle as well as the 2:3 ratio between the triangles! Lots of interesting relationships there. Like 6 is the mean promotional (aka geometric mean) between 4 and 9!

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