Question

Complete the statements to prove the sum of the interior angles of triangle ABC.

A. Statement: Points A, B, and C form a triangle.
Reason: Given
B. Statement: Let DE be a line passing through B and parallel to AC.
Reason: Definition of parallel lines
C. Statement: m∠1=m∠24 and m∠3=m∠25
Reason: Alternate Interior Angles Theorem
D. Statement:m∠24+m∠2+m∠25=180°
Reason: Definition of a straight line

Answer 1

The sum of the interior angles of triangle ABC can be proved using given statements and the Alternate Interior Angles Theorem.

Step-by-step explanation:

To prove the sum of the interior angles of triangle ABC, we can use the following statements:

A. Statement: Points A, B, and C form a triangle. Reason: Given

B. Statement: Let DE be a line passing through B and parallel to AC. Reason: Definition of parallel lines

C. Statement: m∠1=m∠24 and m∠3=m∠25 Reason: Alternate Interior Angles Theorem

D. Statement: m∠24+m∠2+m∠25=180° Reason: Definition of a straight line

Using these statements, we can conclude that the interior angles of triangle ABC add up to 180 degrees.