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 Quadrilateral Hierarchy knowledge point
A rhombus is defined as a quadrilateral with four congruent sides.

Identify quadrilateral properties

Using the Quadrilateral Properties knowledge point
Since a rhombus is a special type of parallelogram, it inherits all properties of a parallelogram while having unique properties regarding its sides and diagonals:

1. If a quadrilateral is a rhombus, then all four of its sides are congruent.
2. If a parallelogram is a rhombus, then its diagonals are perpendicular.
3. If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

Label the diagrams

For the three conditional statements in Question 2, we label the corresponding rhombus diagrams to visually represent each property:

• First diagram (four congruent sides): Place identical tick marks on all four sides.
• Second diagram (perpendicular diagonals): Draw both diagonals intersecting at a right angle symbol (\(90^\circ\)).
• Third diagram (bisected opposite angles): Draw both diagonals and add matching angle arc marks to show that each diagonal splits the vertex angles into two equal halves.

Answer:

Question 1

Definition of a Rhombus:
A rhombus is a quadrilateral with four congruent sides.

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Question 2

Properties of Rhombuses:

1. If a quadrilateral is a rhombus, then it has four congruent sides.

• Labeling: Place identical tick marks on all four outer sides of the first rhombus diagram.

1. If a parallelogram is a rhombus, then its diagonals are perpendicular.

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

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

• Labeling: Draw the diagonals inside the third rhombus diagram and place matching angle arc marks at the split vertex angles to show they are congruent.