Warm Up 1. 2. With a partner, make as many different sketches as you can to represent this statement: AB and AC both bisect <DAE.

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Presentation transcript:

Warm Up With a partner, make as many different sketches as you can to represent this statement: AB and AC both bisect <DAE

1.6 Paragraph Proofs Paragraph Proofs: used in journals, more advanced math, and other areas of study

Given : <O 67.5° <P 67°30’ Prove <O = <P Proof: Since there are 60 minutes in 1 degree, and 30 minutes equals one half a degree, 67°30’ equals 67.5°. Since <O and <P have the same measure, they are =. O P

Given: diagrams shown Prove: <FEH = <JKM D F EH MK J Work: X + 3x = 180 4x = 180 x = 45 3x = 135 3x  xx 135 

Proof: <DEH is a straight angle. Therefore, a straight < m =180 . Then using algebra, m<def + m<FEH = 180 , then m<FEH = 135 . Since <‘s with the same measure are =, <FEH and <JKM are = because they are each 135 

Given: <D = 90  <E is obtuse Prove: <D = <E JUST ONE MORE!!! I PROMISE

Is this conclusion true? This conclusion is false! Since <E is obtuse, its measure is greater than 90. Since <D and <E have different measures, they are not congruent!