![]() Just be sure to avoid using cheap reasons in your proofs. They would all be valid (assuming they did it right), though they might have taken different steps along the way. If you put three mathematicians in a room and have them prove the same theorem, you will probably get three different proofs. Keep in mind that there is more than one way to construct a proof. MABE + mEBC = mABC, mCBF + mFBD = mCBD, and mEBC + mCBF = mEBF Let's see how it all unfolds.ĪBC and CBD are adjacent supplementary angles BE bisects ABC, and BF bisects CBD Because you will be breaking up angles, the Angle Addition Postulate might be useful. Your game plan: You'll need some definitions in this proof: supplementary angles, right angles, and angle bisectors. Interpret what to prove in terms of the picture. For instance, 95° and 85° are supplementary angles. The supplementary angle neednt be adjacent to every other, but its sum should be adequate to 180 degrees. ABC and CBD are adjacent supplementary angles BE bisects ABC, and BF bisects CBD. In Math’s, two angles are said to be supplementary, when the angles add up to 180 degrees. Interpret the given information in terms of the picture. Theorem 9.6: The bisectors of two adjacent supplementary angles form a right angle.Example 7: Prove that the bisectors of two adjacent supplementary angles form a right angle.And you'll prove it.įigure 9.7 ABC and CBD are adjacent supplementary angles BE bisects ABC, and BF bisects CBD. If you construct the bisectors of each of these two angles, then together the bisectors will form a new angle. ABC and CBD are adjacent supplementary angles. Now that you're starting to crank out those formal proofs, it's time to open things up and see how you perform on the open road. ![]() ![]() And there's always algebra.ĪBC is acute, ad ABC and CBD are supplementary. Because you'll be dealing with inequalities (acute angles have measure less than 90º and obtuse angles have measure greater than 90º), you might need your definitions of, and you might need our Protractor Postulate. What's the game plan? This proof involves acute, obtuse, and supplementary angles, so you'll probably use their definitions somewhere. Interpret what you are trying to prove in terms of your drawing. You are given ABC and its supplement CBD, with ABC acute. ![]() Interpret what you are given in terms of your drawing. Figure 9.6 ABC and CBD are supplementary angles. ![]()
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