Question

Amanda is writing a proof for the theorem stated below.

Theorem: The sum of interior angles of a triangle is 180°.

She first drew the figure shown below.

Triangle PQR with side PR extended to point S and side PQ extended to point U. Segment QT is drawn parallel to segment PS. Angle PRQ is 1, angle RPQ is 2, angle PQR is 3, angle RQT is 1, angle TQU is 2.

Which theorem will she most likely use in the proof?

Answer 1

well you know that angles 1, 2, and 3 form a straight angle as it's shown on the right of the triangle

Answer 2

so

m < 1 + m < 2 + m < 3 = 180

Answer 3

now you also know that the angle 1 near point R is the same angle 1 near Q

so this tells us that they are congruent angles

Answer 4

you can do the same for angles 2 and 3

so because m < 1 + m < 2 + m < 3 = 180 from the straight angle

and because you can transfer the angles (they are congruent), you can say


sum of interior angles of triangle = 180 because Supplements of congruent angles are congruent.

Answer 5

then again, you could also use the theorem "Corresponding angles formed by parallel lines and their transversal are congruent", so idk