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By Earl William Swokowski

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If you understand all the strategies and tips covered in this chapter and you can follow every step of this proof, you should be able to handle any proof they throw at you. 50 Geometry Essentials For Dummies Statements Reasons 1) BD ⊥ DE BF ⊥ FE 1) Given. 2) ∠BDE is a right angle ∠BFE is a right angle 2) If segments are perpendicular, then they form right angles. 3) ∠BDE ≅ ∠BFE 3) If two angles are right angles, then they’re congruent. 4) ∠1 ≅ ∠2 4) Given. 5) ∠3 ≅ ∠4 5) If two congruent angles are subtracted from two other congruent angles, then the differences are congruent.

6) TB bisects ∠LTR 6) If a ray divides an angle into two congruent angles, then it bisects the angle (definition of bisect). Subtraction theorems Each of the following subtraction theorems corresponds to one of the addition theorems. ✓ Segment subtraction (three total segments): If a segment is subtracted from two congruent segments, then the differences are congruent. ✓ Angle subtraction (three total angles): If an angle is subtracted from two congruent angles, then the differences are congruent.

Y P 10 Q 4 R S 10 T 4 U A E I O U Figure 2-6: Adding congruent things to congruent things. If and are congruent and and are congruent, is obviously congruent to , right? then And if ∠AYE ≅ ∠UYO (say they’re both 40°) and ∠EYI ≅ ∠OYI (say they’re both 20°), then ∠AYI ≅ ∠UYI (they’d both be 60°). Now for a proof that uses segment addition: M D X C V Impress me: What year is MDXCVI? Really impress me: What famous mathematician (who made a major breakthrough in geometry) was born in this year? I’ve put what amounts to a game plan for this proof inside the following two-column solution, between the numbered lines.

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