TIPS FOR STUDENTS: A few tips and tricks for learning geometry (Part-2)

Sep 07, 2017

We did say in part 1 of this article that we’ll be coming up with a part 2 ASAP. So here it is as promised. Let’s begin.

6. Recognize basic symbols used in geometry problems

When you start learning geometry for the very first time in your life, the variety of symbols can get quite overwhelming. Nevertheless, learning the meaning of each and every one of them, in particular, make things easier for you in the nearly foreseeable future. So here you go:

  • A small triangle symbol (e.g. △) represents the different properties of a triangle.

  • A small angle symbol (e.g. ∠) represents the different properties of an angle. A right angle, on the other hand, is represented by the ∟symbol.__

  • Letters with a small line over them (such as AB) represents the different properties of a line segment.

  • “2 vertical lines” (such as ||) symbol signifies that 2 lines are parallel to one another.

  • A wavy line symbol (such as ~) signifies that 2 shapes are similar to one another.

  • An equal sign with a wavy line on top (such as ≅) symbolizes congruency i.e. two shapes are congruent to one another.

For more details on geometrical symbols, you may refer to this article, in particular.

7. Comprehend the different properties of lines and line segments in precise details

Let’s start this topic off with a simple difference between a line and a line segment.

A line is straight and can extend indefinitely in both directions without any limitation. This is why lines are drawn with an arrow to indicate that they can continue on and on and on. A line segment, on the other hand, has a beginning and an end point.

Lines can be perpendicular, parallel as well as intersecting to one another on basis of the given conditions. Let’s go through a few properties now that you should remember in through details:

  • Two lines that are parallel to one another can NEVER intersect each other at any given point in time.

  • Two lines that are perpendicular to each another form a 90° angle with one another.

  • Intersecting lines are the ones that cross each other like an “X.” Intersecting lines can be perpendicular to each other, but they can NEVER be parallel to one another.

8. Write down the things given and the things to be found/proven at the start of your solution

When you are starting on a solution to a geometrical problem, it’s advisable to write down the things given and the things that need to be found/proven at the start of the problem itself for an easy reference.

We’ll explain this with an example for easier comprehensibility. So here it goes,

Problem: In a triangle ABC, BAC= 54°, ABC= 25°, find ACB.

Your approach should be like:

Given: ∠BAC= 54°, ABC= ∠25°.

RTF (Required to be found)= ∠ACB.

Then you should start on your solution.

A simple practice like that can help to reduce a lot of silly mistakes that can occur as a result of repeated reference to the question paper or the book.

9. Understand the triangles well so that you can identify them in a jiffy

There are 3 different types of triangle, and these 3 are equilateral, scalene and isosceles.

To identify them in a jiffy, you need to keep a few things in mind. These can also help you in your geometrical problem-solving procedures. Take a peek.

  • A scalene triangle has no identical (congruent) sides and no identical angles.

  • An isosceles triangle has two identical sides and two identical angles at the very least, and another unequal side and angle.

  • An equilateral triangle has 3 identical sides and 3 identical angles.

A few more triangle trivia…

  • If you look closely, you will notice that an equilateral triangle’s also an isosceles triangle. That’s because it DOES have 2 congruent sides.

  • Triangles can also be classified on the basis of their angles, and those are acute, obtuse and right angle triangle.


 

So that brings the 2nd part of this article to a close. The 3rd and the final part is going to follow in the next few days. Adieu!

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