Rhombus and Square - Interactive Activity

A rhombus is a parallelogram with four congruent sides, and a square is both a rectangle and a rhombus at once. These activities let you drag a rhombus into new shapes and watch its properties stay true, name the shape or the property a picture shows, and build complete solutions one step at a time.

Definitions and Main Ideas

A rhombus is a parallelogram with four congruent sides, perpendicular diagonals, and diagonals that bisect the opposite angles. A square is the most specialized member of the family: it is both a rectangle and a rhombus, so it has every property of a parallelogram, a rectangle, and a rhombus at once. This lesson adds those properties to the family tree and uses them to solve for angles and lengths.

Vocabulary

Rhombus: A parallelogram with four congruent sides. Its diagonals are perpendicular and bisect the opposite angles.
Square: A parallelogram that is both a rectangle and a rhombus: four congruent sides and four right angles.
Perpendicular: Intersecting at right angles. The diagonals of a rhombus are perpendicular, written with the symbol ⊥.
Angle Bisector: A ray or segment that divides an angle into two congruent angles. Each diagonal of a rhombus bisects the two opposite angles it connects.

Main Ideas

A rhombus has all five properties of a parallelogram, plus four congruent sides.
The diagonals of a rhombus are perpendicular (they intersect at right angles).
Each diagonal of a rhombus bisects the opposite angles — it splits each angle it touches into two congruent parts.
The diagonals of a rhombus cut it into four congruent right triangles.
A square combines both lists: four right angles and congruent diagonals from the rectangle, four congruent sides and perpendicular, angle-bisecting diagonals from the rhombus.
On the family tree, the square sits below both the rectangle and the rhombus because it inherits the properties of each.

The Polygon Family Tree

Properties are inherited as we move down the tree. The highlighted shapes, Rhombus and Square, are the shapes in this lesson.

Rhombus Explorer

What to do: Drag the orange handle at B or the purple handle at D. Vertex A stays fixed, the purple handle slides around A so the two sides from A always have the same length, and C is placed so the figure is always a rhombus. Angles are named with three letters — the middle letter is the vertex. Watch the readouts as you drag.

Drag the orange handle at B to change the side length and the angle at A. Drag the purple handle at D to swing the second side around A — its length always matches the first side, so the figure is always a rhombus.

Name the Shape / Name the Property

What to do: Look at the figure and its marks. Some problems ask for the most specific name of the shape; others ask which statement about the figure is true. A first miss gives a hint and another try. The Next problem button cycles through all eight problems in order.

The Next problem button cycles through all eight problems in order.

Build the Solution

What to do: Work each problem one step at a time. Step 1 chooses the relationship or equation that starts the solution. A first miss gives a hint and another try. The gold highlight marks the part the current step asks about, and a part solved in an earlier step is labeled with its found value.

Continue moves to the next step. New problem cycles through all six problems in order.

Your Turn

What to do: Answer all six questions. A first miss gives a hint and another try; after a second miss the answer is shown and explained. Your score counts first-try answers only.

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Rhombus and Square — Mr. J Geometry. All activities on this page run entirely in your browser.