Question

Prove: ∠3 ≅ ∠6

statement justification
line jk is parallel to line lm 1. given
A)∠7 ≅ ∠6 2.
B)∠3 ≅ ∠7 3.
C)∠3 ≅ ∠6 4

Answer 1

The student's question involves a proof that two angles are congruent using properties of parallel lines and angle relationships in geometry. A precise proof cannot be provided without a diagram, but generally, the transitive property of equality is used to deduce congruence.

Step-by-step explanation:

The student is asking about a proof in geometry, specifically to show that two angles, ∠3 and ∠6, are congruent using given information about parallel lines and other angle relationships. The proof likely involves properties of parallel lines, such as alternate interior angles being congruent, corresponding angles being congruent, or the transitive property of angle congruence. Without a specific diagram, it's not possible to provide a full step-by-step proof. However, based on typical reasons used in proofs with parallel lines, the steps to prove that ∠3 ≅ ∠6 might include stating that if ∠7 ≅ ∠6 (given), and ∠3 ≅ ∠7 (given), then ∠3 ≅ ∠6 by the transitive property of equality (as anything equal to the same thing is also equal to one another).

Answer 2

To prove that ∠3 is congruent to ∠6, we can use the transitive property of congruence. Given the information provided: ∠3 ≅ ∠7 and ∠7 ≅ ∠6, we can conclude that ∠3 ≅ ∠6.

Step-by-step explanation:

To prove that ∠3 is congruent to ∠6, we need to provide a series of statements and justifications. Given that line jk is parallel to line lm, we have the following information:

Statement 1: ∠7 ≅ ∠6 (given)

Statement 2: ∠3 ≅ ∠7 (given)

Statement 3: ∠3 ≅ ∠6 (transitive property)

Using the transitive property of congruence, we can conclude that ∠3 is congruent to ∠6.