Polygon is a closed-plane figure bounded by line segments that meet only at their
endpoints.
Equiangular Regular polygon Irregular
Equilateral polygon polygon
polygon
Sides are all Whose angle are Both equilateral Whose side and
congruent all congruent and equiangular angles are not
equal
Naming Polygon and its Parts
A polygon is named using its vertices. The vertices are points A, B, and C. So, the
ABC are 𝐴𝐵 ,𝐵𝐶, 𝐴𝐶
triangle may be called triangle ABC, triangle BCA, or triangle ACB. Sides of triangle
Interior angles of triangle ABC are ∠BAC, ∠BCA, and ∠ABC
1. Polygons are closed plane figures that are formed by
straight line
segments that meet only at their endpoints.
2. Polygons are classified according to the number of
sides
3. Regular polygon are polygons with all of its sides and
angles equal.
4. Squares are quadrilaterals with 4 right angles & have all
sides equal.
5. Pentagon is a five-sided polygon with equal sides and
equal angles.
6. Irregular are polygons that have non-congruent sides.
7. Octagon is an eight-sided polygon with unequal sides.
8. Equilateral Triangle is a three-sided polygon with
equal sides.
a. Convex Polygons:
A convex polygon is a polygon where all interior angles are less than 180
degrees, and no vertices point inward. In other words, a line segment
drawn between any two points in the polygon will always lie inside or on
the boundary of the polygon.
b. Non-Convex (Concave) Polygons:
A non-convex or concave polygon is a polygon that has at least one
interior angle greater than 180 degrees. This type of polygon has at least
one vertex that points inward, and a line segment drawn between some points
within the polygon may pass outside it.
1. Complementary angles are two angles whose measures add up to 90
degrees. For example, if one angle measures 30 degrees, the other angle
must measure 60 degrees to be complementary.
2. Supplementary angles are two angles whose measures add up to 180
degrees. For instance, if one angle measures 110 degrees, the other must
measure 70 degrees to be supplementary.
3. Adjacent angles are two angles that share a common side and a common
vertex, and do not overlap. They are next to each other.
4. A linear pair is a pair of adjacent angles formed when two lines intersect. The angles in a
linear pair add up to 180 degrees.
5. Vertical angles are the pairs of opposite angles made by two intersecting lines. These
angles are always equal to each other.
Polygons:
A polygon is a closed shape with straight sides. Examples include triangles,
quadrilaterals, pentagons, and so on. Each polygon has its unique set of angles.
Exterior Angles of a Polygon: An exterior angle is formed when a side of a
polygon is extended outward. The sum of all exterior angles in any polygon is
always 360 degrees. Remember, exterior angles are crucial in understanding the
properties of polygons.
Adjacent Interior Angles: These are angles inside the polygon that share a
common side. The sum of adjacent interior angles in a polygon is always 180
degrees. This concept helps us analyze the relationships between angles within a
polygon.
Sum of Interior Angles: One essential concept when dealing with polygons is the
sum of interior angles. The sum of interior angles in any polygon can be found using
a simple formula: (n-2) * 180 degrees, where 'n' represents the number of sides in the
polygon.
Regular vs. Irregular Polygons: It's important to differentiate between regular
and irregular polygons. In a regular polygon, all sides and angles are equal. On the
other hand, irregular polygons have sides and angles of varying lengths and measures.
Exterior Angles: The exterior angle of a polygon is the angle formed between a
side of the polygon and an extension of an adjacent side. The sum of exterior angles in
any polygon is always 360 degrees.
The fundamental operations on rational numbers are: Addition: Combine
fractions by finding a common denominator and adding the numerators.
Subtraction: Subtract fractions by finding a common denominator and subtracting
the numerators. Multiplication: Multiply fractions by multiplying the numerators and
denominators. Division: Divide fractions by multiplying the first fraction by the
reciprocal of the second fraction.
Adding and subtracting rational numbers with various denominators
In the case of rational numbers with different denominators, the addition operation
is performed by finding the LCM, multiplying by the quotient and conversion into
rational numbers with the same denominator.
Step 1: The denominators in the given numbers are different. To get the common
denominator, calculate the LCM of denominators.
Step 2: Using the common denominator, get the equivalent rational number.
Step 3: Because the denominators are now the same, simply add the numerators
before copying the common denominator. Reduce your final answer to the simplest
term possible.
Example: 2/9 + 4/3
LCM is 9. We multiply the second fraction by quotient 3, to get, 12/9
= 2/9 + 12/9
= 14/9
CONVERSION OF FRACTION TO DECIMAL AND VICE VERSA:
To a decimal: Divide the numerator by the denominator. To a fraction: Read the
decimal and reduce the resulting fraction.
Convert to a decimal Divide the numerator by the denominator.
3 ÷ 5 = 0.6.
