I REALLY NEED HELP IN THIS 2 COLUMN PROOF
Complete the two-column proof.
Given: is complementary to .
bisects .
Prove: is complementary to .
Lacking data. Cannot copy and paste here.
To complete the two-column proof, we need to use the given information to arrive at the desired conclusion. Here's a step-by-step guide on how to approach this proof:
Step 1: Start by writing down the given statements and corresponding reasons in the left column of the proof:
Given: AD is complementary to DE (Given)
BD bisects ∠ADE (Given)
Step 2: Identify any definitions, theorems, or postulates that can be applied in this proof. In this case, we can use the definition of complementary angles and the definition of angle bisecting.
Step 3: Use the definitions and properties to make logical deductions in the right column of the proof:
Statements Reasons
1. AD is complementary to DE Given
2. ∠ADE + ∠DEA = 90° Definition of complementary angles
3. BD bisects ∠ADE Given
4. ∠BAD ≅ ∠DAE Definition of angle bisecting
5. ∠BAD = x Given
6. ∠DAE = x Definition of congruent angles
7. x + ∠DEA = 90° Substituting in statements 4 and 6 into statement 2
8. ∠DEA + x = 90° Commutative property of addition
9. x + ∠DEA = ∠DEA + x = 90° Addition property of equality
Step 4: Summarize the proof by stating the conclusion:
Conclusion: ∠ADE is complementary to ∠DEA.
By following these steps and using the given information, you should be able to complete the two-column proof successfully.