Question

Select the correct answer from each drop-down menu. Given a rhombus with diagonal, prove that the diagonal bisects the rhombus. In the diagram of rhombus ABCD, a line AC is drawn as a diagonal. Identify the missing statement and reason in the proof. Given a rhombus with diagonal, it follows from the definition of a rhombus that ________. By the reflexive property of congruence, ________. So, by the ________, since corresponding parts of congruent triangles are congruent, ________. So, by the definition of segment bisector, ________ bisects ________ and ________.

1) ABCD is a parallelogram, diagonals of a parallelogram bisect each other
2) ABCD is a rectangle, diagonals of a rectangle are congruent
3) ABCD is a square, diagonals of a square are perpendicular bisectors of each other
4) ABCD is a trapezoid, diagonals of a trapezoid are congruent

Answer 1

A diagonal of a rhombus bisects it into two congruent triangles.

Step-by-step explanation:

A rhombus is a quadrilateral with all sides congruent. If we draw the diagonal of a rhombus, it will create two congruent triangles. This is because the diagonals of a rhombus bisect each other, meaning they divide each other into two equal parts. By the definition of a rhombus, all sides are congruent. By the reflexive property of congruence, the two sides of each triangle that share the diagonal are congruent. So, by the corresponding parts of congruent triangles are congruent (CPCTC), the other corresponding sides and angles of the triangles are congruent. Finally, by the definition of a segment bisector, the diagonal bisects the rhombus and divides it into two congruent triangles.