Triangles part Two. Congruence and Similarity | iCalculator™ (2024)

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There are lessons in this math tutorial covering . The tutorial starts with an introduction to and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of . you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

  • What is the relationship between the sides and angles in a triangle?
  • What is the range of possible values for the side lengths in a triangle?
  • What are the conditions for two triangles to be congruent?
  • What are the conditions for two triangles to be similar?
  • What is the midline of a triangle?
  • What relationship does the Pythagorean Theorem point out?
  • What are the Euclidean Theorems? What can you find by using them?
  • What is Heron's Formula and why do we use it?
  • What is the relationship between elements in an isosceles triangle?
  • What special feature does a right triangle with angles 30° - 60° - 90° have?

Introduction

Triangles are very extensive in theory and application. Therefore, one tutorial is insufficient to explain all properties of triangles. This tutorial focuses on concepts such as congruence and similarity - concepts that deal with the comparison between triangles. It is a continuation of the previous chapters in a more extended approach.

Congruence and similarity are two important concepts in geometry that describe the relationship between two triangles. Congruence refers to the exact match between two triangles where all the sides and angles are of equal measure. In other words, if two triangles are congruent, they have the same size and shape. On the other hand, similarity refers to the proportionate match between two triangles where the angles are equal but the sides may be of different lengths. In other words, if two triangles are similar, they have the same shape but not necessarily the same size. Both congruence and similarity play an important role in geometry and help us to better understand and analyze geometric figures. Therefore, let's begin to explore this important topic of geometry.

Please select a specific "Triangles part Two. Congruence and Similarity" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Angles and Geometrical Figures Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
18.4Triangles part Two. Congruence and Similarity
Lesson IDMath Lesson TitleLessonVideo
Lesson
18.4.1Relations Between the Angles and the Sides of a Triangle
18.4.2Congruence of Triangles
18.4.3Similarity of Triangles
18.4.4Midline of a Triangle
18.4.5Pythagorean Theorem
18.4.6Euclidian Theorems
18.4.7Heron's Formula
18.4.8Two Special Theorems

Whats next?

Enjoy the "Triangles part Two. Congruence and Similarity" math tutorial? People who liked the "Triangles part Two. Congruence and Similarity" tutorial found the following resources useful:

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  2. Angles and Geometrical Figures Revision Notes: Triangles part Two. Congruence and Similarity. Print the notes so you can revise the key points covered in the math tutorial for Triangles part Two. Congruence and Similarity
  3. Angles and Geometrical Figures Practice Questions: Triangles part Two. Congruence and Similarity. Test and improve your knowledge of Triangles part Two. Congruence and Similarity with example questins and answers
  4. Check your calculations for Angles and Geometrical Figures questions with our excellent Angles and Geometrical Figures calculators which contain full equations and calculations clearly displayed line by line. See the Angles and Geometrical Figures Calculators by iCalculator™ below.
  5. Continuing learning angles and geometrical figures - read our next math tutorial: Quadrilaterals

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    Triangles part Two. Congruence and Similarity | iCalculator™ (2024)

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