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1.6 Paragraph Proofs. State the given State any facts Show work State the conclusion. Just simply explain ALL your steps!. Given: <O = 67.5 o <P = 67 o 30’ Prove: <O = <P

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State the given

  • State any facts
  • Show work
  • State the conclusion
just simply explain all your steps
Just simply explain ALL your steps!

Given: <O = 67.5o

<P = 67o 30’

Prove: <O = <P

Proof: It is given that <0= 67.5o and <P= 67o 30’. Since there are 60 minutes in 1 degree, 67o 30’ equals 67.5o. Since <O and <P have the same measure, they are congruent.

sometimes you ll have to do some math
Sometimes you’ll have to do some math…

D

Given: Diagram as Shown

Prove <DBC = <E

Proof: According to the diagram,

<ABC is a straight angle. Therefore,

2x+x=180

3x=180

X=60

Since <DBC = 60 and <E = 60, the angles are congruent

2x

x

A

B

C

60

E

conclusion is not true
Conclusion is NOT True
  • Provide a counterexample
    • Just show an example as to how the conclusion is NOT true

Given: <1 is acute

<2 is acute

Conclusion: <1 = <2

Proof: This conclusion cannot be proved. For example m<1=20 and m<2=30, they are both acute but not congruent.