If the given is AB is perpendicular to BC, and BC is perpendicular to CD, and you have to prove that angle 7 is congruent to angle 8, how would you write a two column proof for that??
First I'd specify where angles 7 and 8 are.
To write a two-column proof demonstrating that angle 7 is congruent to angle 8 given the information that AB is perpendicular to BC and BC is perpendicular to CD, you can follow these steps:
Step 1: Start by writing down the given statements and reasons in the left column:
Statement Reason
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1. AB ⊥ BC Given
2. BC ⊥ CD Given
Step 2: Identify any vertical angles that can be used in the proof. In this case, angle 7 and angle 8 are vertical angles, since they share the same vertex (B) and are formed by intersecting lines (AB and BC).
Step 3: In the right column, write down the corresponding statements and reasons, including the vertical angles:
Statement Reason
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1. AB ⊥ BC Given
2. BC ⊥ CD Given
3. ∠7 and ∠8 are vertical angles Definition of vertical angles
Step 4: Now, to prove that angle 7 is congruent to angle 8, you can use the fact that if two angles are vertical angles, they are congruent. Add a line to the right column to represent this:
Statement Reason
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1. AB ⊥ BC Given
2. BC ⊥ CD Given
3. ∠7 and ∠8 are vertical angles Definition of vertical angles
4. ∠7 ≅ ∠8 Vertical angles are congruent (congruence property of vertical angles)
Step 5: Your two-column proof is now complete. Angle 7 is congruent to Angle 8 based on the given information and the property of vertical angles.
Note: The numbering of statements may vary depending on your specific proof format. Be sure to follow the proof rules and format preferred by your teacher or textbook.