Similar and congruent triangles

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OER

 * Web resources:
 * This videos is related congruence of triangle.


 * Books and journals
 * Textbooks
 * NCERT Textbooks: Class 7-Chapter 7:Congruence of Triangles, Class 9: Triangles


 * Syllabus documents

Non-OER

 * Web resources:
 * Math is fun


 * Books and journals
 * Textbooks:
 * Karnataka Govt Text book – Class 8 : Part 2
 * Syllabus documents (CBSE, ICSE, IGCSE etc)

Learning objectives

 * Analyse and identify the structure of simple triangles
 * Gather information about the similarities and differences between triangles
 * Comprehend the meaning of congruent triangles - Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.
 * Utilise the newly acquired knowledge in order to solve related problems.
 * Ability to draw congruent triangles
 * Understand the properties of congruent Triangles

Concept 1: What are congruent triangles?
If two triangles are congruent, then each part of the triangle (side or angle) is congruent to the corresponding part in the other triangle.

i.e. CPCTC, which stands for "Corresponding Parts of Congruent Triangles are Congruent". In addition to sides and angles, all other properties of the triangle are the same also, such as area, perimeter, location of centers, circles etc.

Concept # 2. Postulates for congruence of triangles.
Any triangle is defined by six measures (three sides, three angles). Triangles are congruent if:
 * 1) All three corresponding sides are equal in length. SSS (side side side) congruency postulate
 * 2) A pair of corresponding sides and the included angle are equal. -- SAS (side angle side) congruency postulate.
 * 3) A pair of corresponding angles and the included side are equal. -- ASA (angle side angle) congruency postulate.
 * 4) A pair of corresponding angles and a non-included side are equal.-- AAS (angle angle side) congruency postulate.
 * 5) HL (hypotenuse leg of a right triangle) :Two right triangles are congruent if the hypotenuse and one leg are equal.Also known as RHS postulate.

Concept # 5. Tests for similarity
Two triangles are said to be similar if any of the following equivalent conditions hold:
 * 1) The SSS similarity postulate states that if the sides of two triangles are in proportion, then the triangles are similar.
 * 2) The AA similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are said to be similar.
 * 3) SAS Similarity Postulate states, “If an angle of one triangle is congruent to the corresponding angle of another triangle and the sides that include this angle are proportional, then the two triangles are similar.”