Question

Help with a proof please :)?

Answer 1

he figure below shows rhombus ABCD.

Rhombus ABCD with angles 1, 2, 3, and 4 labeled; sides AB, BC, CD, and AD are congruent

The paragraph proof with missing statement proves that the opposite interior angles of the rhombus are congruent

Which statement can be used to fill in the blank space?

The figure is a rhombus which is given. The definition of a rhombus guarantees that Line segment AB and Line segment CD are parallel and that Line segment AD and Line segment BC are parallel. ____________________________________
because they are same side interior angles of two parallel lines cut by a transversal. By the transitive property of equality, ∡1 + ∡2 = ∡2 + ∡3. Using the subtraction property of equality, ∡1 = ∡3. Similarly, ∡2 + ∡3 = 180 and ∡3 + ∡4 = 180 because they are same side interior angles of two parallel lines cut by a transversal. Therefore, using the transitive property of equality, ∡2 + ∡3 = ∡3 + ∡4. Using the subtraction property of equality,
∡2 = ∡4. Since ∡1 = ∡ 3 and ∡2 = ∡4 by the definition of congruence, these opposite angles are congruent.

∡1 + ∡2 = 180 and ∡2 + ∡3 = 180

∡1 + ∡2 = ∡3 + ∡4

∡1 = ∡3

∡1 + ∡2 = ∡2 + ∡3