Question

6 select two options that will complete the sentence below truthfully. if the diagonals of a quadrilateral bisect opposite angles, then the quadrilateral is a _______. a parallelogram b rectangle c square d rhombus

Explanation:

1. Recall the properties of quadrilaterals:

• A rhombus has diagonals that bisect the opposite angles. A square is a special type of rhombus (and also a special type of rectangle and parallelogram).
• A parallelogram has diagonals that bisect each other, but not necessarily bisect the angles (except in the case of a rhombus/ square). A rectangle has diagonals that are equal and bisect each other, but do not bisect the angles (unless it is a square).
• So, a quadrilateral with diagonals bisecting opposite angles must be a rhombus (and since a square is a rhombus, it also satisfies this property).

1. Analyze each option:

• Option A: A general parallelogram's diagonals bisect each other but do not necessarily bisect the angles. So, A is incorrect.
• Option B: A rectangle's diagonals are equal and bisect each other, but do not bisect the angles (unless it is a square). So, B is incorrect.
• Option C: A square is a rhombus (and also a rectangle/parallelogram) and its diagonals bisect the opposite angles. So, C is correct.
• Option D: A rhombus has diagonals that bisect the opposite angles. So, D is correct.

Answer:

C. square, D. rhombus