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Geometry Proofs - 2 Column Proofs

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@AmpleJudgment

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Questions and Answers

What is the proof for Given: 3( x ^ 2) = x + 12, Prove: x = 9?

x = 9 can be proved by solving the equation 3(x^2) = x + 12.

What is the proof for Given: AB || CD, Prove: AC || BD?

AC is parallel to BD based on the properties of parallel lines.

What is the proof for Given: 1 is supplementary to 2 and 3 is supplementary to 2, Prove: 1 is supplementary to 3?

1 + 2 = 180° and 2 + 3 = 180° implies that 1 + 3 = 180°.

What is the proof for Given: EC bisects AED, ED bisects CEB, Prove: 1 = 2?

Angle 1 and angle 2 are equal as both angles are formed from the bisected angles. Signup and view all the answers

What is the proof for Given: AB || CD, M is the midpoint of AB, N is the midpoint of CD, Prove: AM = ND?

AM = ND because M and N are midpoints. Signup and view all the answers

What is the proof for Given: AB || CD; BD = DE, Prove: AD = CE?

AD = CE can be proved using transitive property of congruence. Signup and view all the answers

What is the proof for Given: C is the midpoint of AB, DE || AC, Prove: CB = DE?

CB = DE can be concluded because DE is parallel to AC and C is a midpoint. Signup and view all the answers

What is the proof for Given: Line l bisects XY at point W, D is the midpoint of CE, WY = CD, Prove: XW = DE?

XW = DE can be deduced from the bisection and midpoint properties. Signup and view all the answers

What is the proof for Given: AB = XW, AB = WY, Prove: W is the midpoint of XY?

W is the midpoint of XY because both AB = XW and AB = WY implies that XW and WY are equal. Signup and view all the answers

Study Notes

Geometry Proofs - 2 Column Proofs

Problem 1:
- Given: 3(x + 2) = x + 2 + x + 12
- Prove: x = 9
Problem 2:
- Given: AB ≅ CD
- Prove: AC ≅ BD
Problem 3:
- Given: ∠1 is supplementary to ∠2
- Given: ∠3 is supplementary to ∠2
- Prove: ∠1 ≅ ∠3
Problem 4:
- Given: EC bisects ∠AED
- Given: ED bisects ∠CEB
- Prove: ∠1 ≅ ∠2
Problem 5:
- Given: AB ≅ CD
- Given: M is the midpoint of AB
- Given: N is the midpoint of CD
- Prove: AM ≅ ND
Problem 6:
- Given: AB ≅ CD, BD ≅ DE
- Prove: AD ≅ CE
Problem 7:
- Given: C is the midpoint of AB, DE ⊥ AC
- Prove: CB ≅ DE
Problem 8:
- Given: Line l bisects XY at point W
- Given: D is the midpoint of CE
- Given: WY = CD
- Prove: XW ≅ DE
Problem 9:
- Given: AB ⊥ XW, AB ⊥ WY
- Prove: W is the midpoint of XY

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Description

Test your knowledge of two-column proofs in geometry with this quiz. Each problem requires you to use logical reasoning and known geometric principles to prove the given statements. Challenge yourself to improve your proof-writing skills!