Question

State and prove following theorems:A.I.A. (alt. Interior Angle)CBSE BOARD IX​

Answer 1

Answer:

Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Proof of Alternate Interior Angles Theorem:

Given: l || m

Prove: ∠3≅∠6Statement

Reason

1. l || m Given

2. ∠3≅∠7 Corresponding Angles

Postulate3. ∠7≅∠6 Vertical Angles Theorem4. ∠3≅∠6 Transitive PoC

There are several ways we could have done this proof. For example, Step 2 could have been ∠2≅∠6 for the same reason, followed by ∠2≅∠3. We could have also proved that ∠4≅∠5.

Answer 2

Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Proof of Alternate Interior Angles Theorem:

Given: l || m

Prove: ∠3≅∠6Statement

Reason

1. l || m Given

2. ∠3≅∠7 Corresponding Angles

Postulate3. ∠7≅∠6 Vertical Angles Theorem4. ∠3≅∠6 Transitive PoC

There are several ways we could have done this proof. For example, Step 2 could have been ∠2≅∠6 for the same reason, followed by ∠2≅∠3. We could have also proved that ∠4≅∠5.