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

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

E H M K

J

Work:X + 3x = 180 4x = 180 x = 45 3x = 135

3xx 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!