A pentagram is the simplest regular star polygon. It is made by extending each side of a regular pentagon. There are a total of 10 vertices in a pentagram. A pentagram can either be formed by connecting alternate vertices of a pentagon or by creating five triangles outside the pentagon. There are two types of pentagrams - regular and irregular pentagram. Let's learn more about it in detail.
|2.||Types of Pentagrams|
|3.||Angles in a Regular Pentagram|
|4.||How to Construct a Regular Pentagram?|
|5.||Solved Examples on Pentagram|
|6.||Practice Questions on Pentagram|
|7.||FAQs on Pentagram|
A pentagram is the shape of a five-pointed star polygon. It is also known as a star pentagon due to its shape and the pentagon in its center, which explains the origin of the word pentagram. In the past, the pentagram symbol has also been used as a holy sign to represent goodness, and for protection against evil.
Types of Pentagrams
Like any other polygon, pentagrams can also be classified into two different types. There are two types of pentagrams - regular and irregular.
A regular pentagram consists of a regular pentagon in its center, and 5 congruent isosceles triangles forming the 5 points. A regular pentagram has:
- 5 congruent isosceles triangles; and
- A regular pentagon in the center
The pentagon in the center of an irregular pentagram is an irregular pentagon. The triangles of an irregular pentagram are not congruent. An irregular pentagram has:
- Five triangles which are not congruent; and
- An irregular pentagon in its center.
Angles in a Regular Pentagram
We know that there is a regular pentagon formed in the center of a regular pentagram. Let's discuss the exterior and interior angles formed in a pentagram including their measurements.
Angles of Pentagon
As we have discussed that there is a regular pentagon inside a regular pentagram. So, each interior angle of this regular pentagon = 108º
∠ABC = ∠BCD = ∠CDE = ∠DEA = ∠EAB = 108°
The Supplementary Angles
As seen above, the interior angles of the pentagon in the center are 108°. Therefore, all the respective supplementary angles will be 72°. Now, since all the five triangles of the pentagram are isosceles, their base angles will be congruent. Hence, all the 10 base angles of the five triangles will be 72°.
∠GAB = ∠GBA = ∠HBC = ∠HCB = ∠ICD = ∠IDC = ∠JDE = ∠JED = ∠FEA = ∠FAE = 72°
Interior Angle of Pentagram
The measurement of all five interior angles of a regular pentagram is 36° each. We know that the sum of all the interior angles of a triangle is 180°. Now, let's observe the triangle GAB,
∠G = 180º − (72º + 72º) = 36°
Similarly, all the other angles of the remaining triangles of the pentagram will be calculated in the same way.
∠H = ∠I = ∠J = ∠F= 36°
Tips and Tricks
- You can easily construct a pentagram by extending the sides of a regular pentagon with the help of a ruler; OR
- Draw two diagonals from each vertex of a regular pentagon to construct a pentagram.
How to Construct a Regular Pentagram?
There are many ways in which a regular pentagram can be constructed. However, let us see the two interesting ones.
Inside a Regular Pentagon
A regular pentagram can be constructed inside a regular pentagon by drawing its diagonals. Draw 2 diagonals each from all the 5 vertices of the pentagon. And your pentagram is ready!
Now let us see how to construct a pentagram outside a regular pentagon
Outside a Regular Pentagon
A regular pentagram can be constructed outside a regular pentagon by extending its 5 sides. Extend each side of the pentagon in such a way that they intersect each other as shown. And you make a pentagram again!
- There are 5 congruent isosceles triangles in a regular pentagram.
- There is a regular pentagon inside a regular pentagram.
- A pentagram can be constructed inside and outside a regular pentagon.
Related Articles on Pentagram
Check out these interesting articles on pentagram. Click to know more!
Solved Examples on Pentagram
Example 1: Identify the shape which resembles a pentagram.
The second image resembles a pentagram because it is shaped like a five-pointed star. Therefore, the second image is the answer.
Example 2: State whether the following statements are true or false with reference to a Pentagram:
a) There is a hexagon in the center of a regular pentagram
b) A regular pentagon can be constructed inside a regular pentagram.
c) The pentagram is famous as a magical symbol.
a) False, there is a regular pentagon inside a regular pentagram
b) True, a regular pentagon can be constructed inside a regular pentagram through its diagonals.
c) True, the pentagram is famous as a magical symbol.
FAQs on Pentagram
What is a 3 - D Star called?
In Geometry, a 3-d star is usually referred to as the star polyhedron, which has a star-like visual appearance.
What is a 12 - Sided Star called?
In Geometry, a 12-sided star is called a dodecagram, which can also be called a star polygon with 12 vertices.
What are the Angles of a 5 Point Star?
In a regular pentagram (5-pointed star, NOT Pentagon), the angle in each point is 36°, so the angles in all five points sum to 180°.
How many Lines of Symmetry Does a Regular Pentagram have?
A regular pentagram has 5 lines of symmetry.
How many Congruent Isosceles Triangles does a Regular Pentagram have?
A regular pentagram has 5 congruent isosceles triangles.
Which Pentagon is in the Center of an Irregular Pentagram?
The pentagon in the center of an irregular pentagram is an irregular pentagon.