Geometric Relationships

Geometry is an exciting part of mathematics, where we learn to explore shapes and objects, and the ways in which these are related. In this hub, brought to you by www.tenmarks.com (Online Math Programs), we classify geometric figures such as triangles and polygons into their various types, and learn about their properties. We also explore symmetry and transformations of figures.

To understand this concept better, let us break it into smaller concepts. These concepts are as follows:

1. Angles in Triangles

This topic deals with finding the unknown angles in a triangle using the Triangle Sum Theorem. Below is a sample video which teaches you to solve a typical problem based on this topic.

- The angle measures of a triangle add to 180°. This is known as the Triangle Sum Theorem

- An acute triangle has 3 acute angles

- A right triangle has 1 right angle

- An obtuse triangle has 1 obtuse angle

2. Classification of Polygons

This topic explains the classification of polygons and quadrilaterals. Finding the measures of angles in polygons is also covered in this topic. Below is a sample video which teaches you to solve a typical problem based on this topic.

- A polygon is a closed plane figure formed by three or more segments. A polygon is named by

   the number of its sides

- Find the sum of the angle measures in a polygon by dividing the polygon into triangles

- The angle measures of a triangle add up to 180° (Triangle Sum Theorem)

- An n-gon can be divided into n - 2 triangles. The sum of the angle measures of any n-gon is

   180° (n - 2)

- If all sides and angles of a polygon are congruent, the polygon is known as a regular polygon

3. Congruence

In this topic, we will learn to use properties of congruent figures to solve problems. Below is a sample video which teaches you to solve a typical problem based on this topic.

- Two figures that have the same shape and size are said to be congruent

- If two triangles are congruent, all of their corresponding sides and angles are congruent

-  In a congruence statement, the vertices in the second polygon have to be written in order of

   correspondence with the first polygon

- A correspondence is a way of matching up two sets of objects

- We can start from any vertex to write the congruence statement

4. Coordinate Geometry - Lines and Slopes

In this topic, we will learn to identify polygons in the coordinate plane. Finding the slopes of lines and identification of parallel and perpendicular lines using slopes is also covered in this topic. Below is a sample video which teaches you to solve a typical problem based on this topic.

- Slope is a number that describes how steep a line is.

   Slope = Vertical change/Horizontal change = Rise/Run

- Rise is the number of units we move up or down. It is positive if we move up and negative if

   we move down

- Run is the number of units we move right or left. It is positive if we move right and negative if

   we move left

- If a line rises from left to right, its slope is positive. If a line falls from left to right, its slope is

   negative

- The slope of a horizontal line is 0. The slope of a vertical line is undefined

About the Author:

The ‘TenMarks Instructor’ is an educationist, a teacher, a guru, and a friend – someone available for help with math, learning, curriculums, methodologies, and parenting – whenever you need it. She represents TenMarks Education, Inc., a company passionate about K12 Math Education, which aims to revolutionize the way kids learn, and build a stronger future for today’s generation through a strong foundation in math.

TenMarks – The best way to practice and master math concepts - Offers a variety of personalized, structured summer and year long math programs for grades 3 – 10, mapped to state standards. Intelligent worksheets, hints, video lessons, tests, practice, recommendations and a customized, adaptive curriculum help build, maintain and enhance core math skills.