Common Core Standards: Math
5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Tom Hanks as Forrest in Forrest Gump, Tom Hanks as Ray Peterson in The 'Burbs, and Tom Hanks as Chuck Noland in Cast Away. Congruent or similar?
Well, they are technically different characters in very different movies. So they'd probably best be described as similar. But based on Hanks's fixation with urinating on camera, they certainly have congruent characteristics.
To truly test for congruence versus similarity, we'd need to evaluate them based on more specific terms. Like which side of the discussion about choosing an even numbered-urinal they come down on. Or their angle on preventing splashback.
Enough pee jokes? Yes, thanks.
The criteria to determine whether triangles are congruent or similar include proportionality or congruency of side lengths and congruency of angles. Fortunately, students don't have to check all three sides and all three angles every time they want to test for congruency or similarity. That would make the process rather inefficient.
And if we've said it once, we've said it a million times: mathematicians thrive on efficiency.
There are several ways to combine the side length proportionality or congruency and angle congruency to check for triangle congruency or similarity. They're various combinations and permutations of the letters S (for side) and A (for angle) and students should already be familiar with them. In fact, they should have mastered these congruency versus similarity tests for triangles.
The Tom Hanks character congruency versus similarity test, however, still needs some work.
- Square: Find the Diagonal
- 3-4-5 Triangle: Find the Remaining Side
- 3-4-5 Triangle: Find the Hypotenuse
- 3-4-5 Triangle: Find the Area
- Equilateral Triangle: Find the Area Given the Altitude
- Rectangle: Find the Diagonal
- 30-60-90 Triangle: Find the Hypotenuse
- 30-60-90 Triangle: Find the Area Given Two Sides
- 30-60-90 Triangle: Find the Area Given an Angle
- 30-60-90 Triangle: Find Another Side Given the Area