Question

Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of △ABC is 180°.

Statement: Points A, B, and C form a triangle.
Reason: Given.
Statement: Let D be a line passing through B and parallel to AC.
Reason: Definition of parallel lines.
Statement: ∠3 = ∠5 and ∠1 = ∠4
Reason: Corresponding angles.
Statement: m∠1 + m∠2 + m∠3 = 180°
Reason: Angle addition and definition of a straight line.
Statement: m∠1 + m∠2 + m∠3 = m∠4 + m∠5 + m∠3
Reason: Substitution.

Answer 1

To prove that the sum of the interior angles of a triangle is 180°, we can use the given statements and reasons.

Step-by-step explanation:

In order to prove that the sum of the interior angles of a triangle is 180°, we can use the given statements and reasons.

Statement 1: Points A, B, and C form a triangle. (Given)

Statement 2: Let D be a line passing through B and parallel to AC. (Definition of parallel lines)

Statement 3: ∠3 = ∠5 and ∠1 = ∠4. (Corresponding angles)

Statement 4: m∠1 + m∠2 + m∠3 = 180°. (Angle addition and definition of a straight line)

Statement 5: m∠1 + m∠2 + m∠3 = m∠4 + m∠5 + m∠3. (Substitution)