- Station 3: Conditional Statements
- Original Statement: If you play a guitar, then you play a stringed instrument.
- Converse: If you play a stringed instrument, then you play a guitar. (False; counterexample: playing a violin).
- Inverse: If you do not play a guitar, then you do not play a stringed instrument. (False; counterexample: playing a cello).
- Contrapositive: If you do not play a stringed instrument, then you do not play a guitar. (True).
- Station 5: Properties from Algebra
- Step 1: 4x - 7 = 3(x - 2) → Reason: Given.
- Step 2: 4x - 7 = 3x - 6 → Reason: Distributive Property.
- Step 3: x - 7 = -6 → Reason: Subtraction Property of Equality (subtract 3x from both sides).
- Step 4: x = 1 → Reason: Addition Property of Equality (add 7 to both sides).
- Station 8: Proof
- Statement 1: BD is an angle bisector of ∠ABC. → Reason: Given.
- Statement 2: ∠ABD ≅ ∠CBD. → Reason: Definition of Angle Bisector.
- Statement 3: m∠ABD = m∠CBD. → Reason: Definition of Congruent Angles.
- Statement 4: m∠ABD + m∠CBD = m∠ABC. → Reason: Angle Addition Postulate.
- Statement 5: m∠ABD + m∠ABD = m∠ABC. → Reason: Substitution Property (replace m∠CBD with m∠ABD).
- Statement 6: 2m∠ABD = m∠ABC. → Reason: Simplify (Combine Like Terms).
- Statement 7: m∠ABD = ½ m∠ABC. → Reason: Division Property of Equality (divide both sides by 2).
Parent Tip: Review the logic above to help your child master the concept of geometry proof worksheets with answers.
