Question

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

Answer 1

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. ∡1 + ∡2 = 180 and ∡2 + ∡3 = 180 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, ____________________________________. 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 = ∡3 + ∡4

∡1 + ∡2 = 180 and ∡2 + ∡3 = 180

∡1 + ∡2 = ∡2 + ∡3

∡1 = ∡3

Answer 2

@ganeshie8 @dpaInc @KingGeorge @ParthKohli @robtobey

Answer 3

@AravindG