Question

your turn

1. draw and explain in your own words the following.

definition of a rhombus

1. according to the properties of rhombuses, label the rhombuses below appropriately.

properties of rhombuses
if a quadrilateral is a rhombus, then
if a parallelogram is a rhombus, then
if a parallelogram is a rhombus, then

Explanation:

Define a rhombus

Using the Rhombus Definition knowledge point

$$ \text{A rhombus is a quadrilateral with four congruent sides.} $$

Identify quadrilateral property

Using the Rhombus Properties knowledge point

$$ \text{If a quadrilateral is a rhombus, then it has four congruent sides.} $$

Identify diagonal perpendicularity property

Using the Rhombus Properties knowledge point

$$ \text{If a parallelogram is a rhombus, then its diagonals are perpendicular.} $$

Identify diagonal angle bisection property

Using the Rhombus Properties knowledge point

$$ \text{If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.} $$

Answer:

Question 1

Definition of a Rhombus:

• Explanation: A rhombus is a quadrilateral with four congruent sides.
• Drawing: A four-sided figure where all four sides are marked with equal tick marks to show they are of equal length.

---

Question 2

Properties of Rhombuses:

1. If a quadrilateral is a rhombus, then <blank>it has four congruent sides.</blank>

• Labeling the first rhombus: Mark all four outer sides with identical single tick marks to show they are congruent.

1. If a parallelogram is a rhombus, then <blank>its diagonals are perpendicular.</blank>

• Labeling the second rhombus: Draw the two diagonals intersecting inside the rhombus and mark their intersection with a right-angle symbol (\(90^\circ\)).

1. If a parallelogram is a rhombus, then <blank>each diagonal bisects a pair of opposite angles.</blank>

• Labeling the third rhombus: Draw the two diagonals and mark the split angles at each vertex with matching arc symbols to show they are divided into two equal angles.