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Congruent Triangles
- SSA Theorem?
- AAA Challenge
- Construct a Congruent Angle
- SSA Counterexample
- Visual Evidence Disproving SSA
- Disprove AAA
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Congruent Triangles
Sonja Howland, Sep 25, 2017
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1. SSA Theorem?
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2. AAA Challenge
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3. Construct a Congruent Angle
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4. SSA Counterexample
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5. Visual Evidence Disproving SSA
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6. Disprove AAA
SSA Theorem?
Thus far, we've learned several theorems that allow us to conclude 2 triangles are congruent.
Here's the list of discoveries we've made thus far:
SAS Theorem
SSS Theorem
ASA Theorem
AAS Theorem (easily proven simply by finding the each triangle's 3rd angle and then using ASA Theorem.)
HL Theorem (For Right Triangles: Easily Proven since we can just use the Pythagorean Theorem to solve for the other leg and then use the SSS Theorem.)
Yet MANY students ask, "What about SSA?"
That is, if 2 sides and a non-included-angle of one triangle are congruent to 2 sides and a non-included-angle of another triangle, are the triangles themselves congruent?
Interact with BOTH applets for a few minutes and see if you can answer this question for yourself. As you do, feel free to move the WHITE POINTS anywhere you'd like!
Feel free to adjust the "a" and "b" sliders as well.
SSA? (Applet 1)
SSA? (Applet 2)
Quick (Silent) Demo
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