Essentials of Geometry

Introduction to Basic Concepts of Geometry

​B.S.ED. - MATHEMATICS 1B
BEJEC - BONSUKAN - BERING - CONSOLACION - CORTES - GENAYAS - GORDOVE - INDIOLA - MIASCO - TANGAG

Objectives

At the end of the lesson, students should be able to:

1.Identify and classify angles, quadrilaterals, and triangles.

2.Understand the properties of points, lines, and planes.

3.Recognize the parts of a circle.

4.Apply set operations in solving simple problems.

​Topic Outline:

1. Points and Lines

2. Types of angles

3. Types of Triangles

4. Types of Quadrilateral

5. Parts of the Circle

6. Set Operations

​a point represents a specific location in space.

​​Point

a straight path that extends infinitely in both directions.

Line

a part of a line that starts at one endpoint and extends infinitely in one direction.

Ray

​a part of a line that has two endpoints.

Line Segment

1. Points and Lines

two or more lines that are in the same plane and never intersect, no matter how far they are extended.

​​1. Points and Lines

two lines that intersect at a right angle (90°).

Perpendicular Lines

two or more lines that cross each other at a single point.

Intersecting Lines

​​Parallel Lines

An angle that measures exactly 90°.

​​Right Angle

An angle that measures less than 90°.

​​Acute Angle

​An angle that measures more than 90° but less than 180°.

​​Obtuse Angle

​​2. Types of Angles

An angle that measures more than 180° but less than 360°.

Reflex Angle

An angle that measures exactly 180°.

Straight Angle

An angle that measures exactly 360°. It represents a full turn or one complete rotation.

​​Full Rotation

​​2. Types of Angles

​A quadrilateral where opposite sides are both parallel and equal in length. The opposite angles are also equal.

​​3. Types of Quadrilaterals

​A parallelogram where all angles are right angles (90°). The opposite sides are equal, and its diagonals are of equal length.

​​Rectangle

A special type of rectangle where all four sides are equal. It combines the properties of a rectangle and a rhombus.

​​Square

​​Parallelogram

A parallelogram where all four sides are of equal length. Opposite angles are equal, but the angles are not necessarily 90°.

​​3. Types of Quadrilaterals

A quadrilateral with only one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are the legs.

​​Trapezoid

​​Rhombus

All three angles are less than 90°. Example: A triangle with angles of 50°, 60°, and 70°.

​4. Types of Triangles

One of its angles is exactly 90°. The side opposite the right angle is the longest and is called the hypotenuse.

Right Triangle

One of its angles is greater than 90°. Example: A triangle with angles of 30°, 40°, and 110°.

​​Obtuse Triangle

Acute Triangle

By Angle:

No sides are of equal length, and all angles are different.

​4. Types of Triangles

Two sides are of equal length, and the angles opposite these sides are also equal.

Isosceles Triangle

All three sides are equal in length, and all three angles measure 60°.

​​Equilateral Triangle

Scalene Triangle

By Sides:

Radius:

The distance from the center of the circle to any point on the circle. It is half the length of the diameter.

Diameter:

A line segment passing through the center and connecting two points on the circle. It is the longest chord and equals twice the radius.

Circumference:

The distance around the circle (its perimeter). It is calculated as C=2πrC = 2\pi rC=2πr, where rrr is the radius.

​5. Parts of the Circle

Chord:

A line segment connecting two points on the circle. Unlike the diameter, it does not necessarily pass through the center

Arc:

A part of the circle's circumference. Example: A semicircle is an arc representing half of the circle.

Sector:

A region of the circle enclosed by two radii and an arc. It looks like a "slice of pizza.

​5. Parts of the Circle

The union of sets A and B includes all elements that are in A, B, or both.

​​6. Set Operations

The intersection of sets A and B includes only the elements that are common to both sets.

Intersection (∩):

The difference of sets includes elements that belong to one set but not the other.

​The complement of a set includes all elements not in the set, within a universal set.

Difference
( A - B ):

Union ( ∪ ):

Complement ( A’ ):

Thank you!