Question

Sheri wants to prove that the sum of the interior angles in a triangle is 180°. To do this, she sketched out a pair of parallel line segments and formed a triangle in between those lines. She then wrote the first few statements to try to prove this.

Two line segments intersecting at the first parallel line and forming an angle 2. The angles below the first parallel line and left to the vertex of the triangle is 1 and right is 3. The angles above the second parallel line and vertex of the triangle is 4 and inside the triangle is 5, and the angle right to another vertex is 7 and inside the triangle is 6.

Statement Number Statement
1
∠
1
+
∠
2
+
∠
3
=
180
°
2
∠
2
≅
∠
4
3
∠
3
≅
∠
6
4
∠
4
+
∠
6
=
180
°
Select TWO of the statements that must be true in the proof.

A.
statement 1

B.
statement 4

C.
statement 3

E.
statement 2

Answer 1

Answers: C and E — statements 3 and 2.

Reason: With the two parallel lines the angles labeled 2 and 4 are congruent (alternate interior/corresponding), and likewise 3 and 6 are congruent. Statement 1 is the theorem to be proved (not an allowed given), and statement 4 is false as written — the straight-line relation involves ∠4 + ∠5 + ∠6 = 180°, not ∠4 + ∠6 = 180°.