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An Intro. to Differential Geometry With Applns to Elasticity by P. Ciarlet

By P. Ciarlet

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Additional info for An Intro. to Differential Geometry With Applns to Elasticity

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No worries — just jump to the end of the proof and work backward. Okay, so picking up where I left off on this chapter’s proof: You’ve completed five lines of the proof, and you’re up to ∠3 ≅ ∠4. Where to now? Going forward from here might be a bit tricky, so work backward. You know that the final line of bisects ∠ABC. the proof has to be the prove statement: Now, if you think about what the final reason has to be or what the second-to-last statement should be, it shouldn’t be too hard to see that you need to have two congruent angles to conclude that a larger angle is bisected.

Complementary and Supplementary Angles Ready for your first theorems? 28 Geometry Essentials For Dummies ✓ Complements of the same angle are congruent. If two angles are each complementary to a third angle, then they’re congruent to each other. ) ✓ Complements of congruent angles are congruent. If two angles are complementary to two other congruent angles, then they’re congruent (four total angles). ✓ Supplements of the same angle are congruent. If two angles are each supplementary to a third angle, then they’re congruent to each other.

The following proof uses Like Divisions: N O D E A L Here’s a possible game plan: What can you do with the first given? If you can’t figure that out right away, make up lengths , , and . Say that and are both 12 and that for is 6. That would make both and 18 units long. Then, because both of these segments are bisected by their midand must both be 9. That’s a wrap. points, Statements Reasons 1) ND ≅ EL 1) Given. 2) NE ≅ DL 2) If a segment is added to two congruent segments, then the sums are congruent.

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