Pentagon vs Star Quiz: Test Yourself
Five quick questions on pentagon vs star. Pick an answer to get instant feedback.
Flip Cards: Quick Review
Hover over a card, or tap it on mobile, to see the meaning.
A five-sided polygon whose sides never cross.
“Each angle of a regular pentagon is 108°.”
A five-pointed star drawn with five crossing lines.
“She drew a pentagram in one stroke.”
108° is each corner of a regular pentagon. 36° is each tip of a regular pentagram.
“Same five points, very different angles.”
The five-sided US defense headquarters building in Arlington, Virginia.
“The Pentagon is shaped like a pentagon.”
The pentagon vs star question trips people up because both shapes involve the number five and are closely related. In fact, you can build a star from a pentagon. The two shapes still look and behave very differently. This guide explains each one, compares their angles and shows how they connect.
| Term | Meaning | Part of speech / Category | Example sentence |
|---|---|---|---|
| Pentagon | A polygon with five straight sides and five corners | Noun / Geometry | She traced a regular pentagon with a ruler. |
| Pentagram | A five-pointed star drawn with five straight lines | Noun / Geometry (star polygon) | The pentagram can be drawn without lifting the pen. |
| Star (shape) | A figure with points radiating from a center, usually five or more | Noun / Shape | The flag has a white star on a blue field. |
| The Pentagon | The US defense headquarters building in Arlington, Virginia | Proper noun / Building | Officials met at the Pentagon on Monday. |
What is a pentagon?
A pentagon is a closed flat shape with five straight sides and five corners. The prefix “penta-” means five. The sides of a pentagon never cross each other, and its five interior angles always add up to 540 degrees.
In a regular pentagon, all sides and angles are equal, and each interior angle is 108 degrees. A regular pentagon is always convex. Irregular pentagons can have unequal sides and angles, and some can be concave.
What is a star shape?
A star shape has points radiating from a center. The most familiar one has five points and is called a pentagram. It is a five-pointed star polygon drawn with five straight lines that cross each other. The lines connect every second point of a regular pentagon, which geometers write as {5/2}.
In a regular pentagram, each tip has an angle of 36 degrees. It is made of five identical thin triangles around a small pentagon in the middle. Not every star has five points, though. A six-pointed star, for instance, is a hexagram.
Pentagon vs star: what is the real difference?
The real difference is how the lines behave. A pentagon’s sides form a simple closed shape and never cross. A pentagram’s lines cross each other, which creates the points.
- Outline: A pentagon looks like a compact five-sided shape. A pentagram looks spiky.
- Angles: Each corner of a regular pentagon is 108 degrees. Each tip of a regular pentagram is 36 degrees.
- Lines: Pentagon sides stay apart. Pentagram lines intersect.
- Drawing: A pentagram can be drawn in one continuous stroke.
- Shared features: Both regular shapes have five lines of symmetry.
How are a pentagon and a pentagram related?
They are built from each other. Draw the five diagonals of a regular pentagon, and those diagonals form a pentagram. Extend the sides of a regular pentagon until they meet, and you also get a pentagram. Going the other way, a regular pentagram encloses a smaller regular pentagon in its center, and that pentagon’s diagonals form a smaller star again. This repeating pattern is connected to the golden ratio.
Is the Pentagon building a pentagon?
Yes. The Pentagon is the headquarters of the US Department of Defense in Arlington, Virginia, and it is named for its five-sided shape. When written with a capital P, it usually means the building or the military leadership. Written in lowercase, “pentagon” means the geometric shape.
How can you remember which one to use?
Ask whether the lines cross. If five straight sides close up neatly without crossing, it is a pentagon. If the lines cross and make sharp points, it is a star, specifically a pentagram.
Common mistakes with pentagon vs star
- ✗ A five-pointed star is a pentagon.
✓ A five-pointed star is a pentagram. A pentagon is the plain five-sided shape. - ✗ The tips of a regular star measure 108 degrees.
✓ Regular pentagon corners are 108 degrees, and regular pentagram tips are 36 degrees. - ✗ Every star has five points.
✓ Stars can have many numbers of points. A six-pointed star is a hexagram. - ✗ The sides of a pentagon cross each other.
✓ A pentagon’s sides never cross, while a pentagram’s lines do. - ✗ The Pentagon building is shaped like a star.
✓ The Pentagon building has five sides, like a pentagon.
Memory tricks
- Penta = five. Both shapes are built on five points, but only one has crossing lines.
- Gram = line. The “gram” in pentagram comes from a Greek word for line, so a pentagram is five lines.
- Corners vs tips. A pentagon has corners (108 degrees) and a star has tips (36 degrees).
FAQ
What is the difference between a pentagon and a star?
A pentagon is a five-sided shape whose sides never cross. A five-pointed star, called a pentagram, is drawn with five lines that cross each other and form five sharp points.
Is a five-pointed star a pentagon?
No. A five-pointed star is a pentagram. It is closely related to a pentagon because it is made from a pentagon’s diagonals, but it is a different shape.
What is a five-pointed star called?
A five-pointed star is called a pentagram. In geometry it is also described as the star polygon 5/2.
How many degrees are in each point of a pentagram?
Each point of a regular pentagram has an angle of 36 degrees. Each interior angle of a regular pentagon is 108 degrees.
Is the Pentagon building a pentagon?
Yes. The Pentagon, the US defense headquarters in Arlington, Virginia, has five sides and is named for the pentagon shape.
Conclusion
In the pentagon vs star comparison, remember that a pentagon is a five-sided shape with corners and a star is a spiky shape with tips. The pentagram star is built from the pentagon’s diagonals, so the two are close relatives. Share this with someone who mixes these up.