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Proving Triangles Congruent

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Whiteboardmaths.com © 2004 All rights reserved

Congruent Triangles Remember: Two shapes are congruent if all sides and angles in one, are equal to the sides and angles in the other. Congruent triangles are of particular importance in mathematics because they enable us to determine/prove many geometrical properties/theorems. Euclid of Alexandria In his book “The Elements” Euclid proved four theorems concerning the conditions under which triangles are guaranteed to be congruent. He used some of these theorems to help establish proofs of other important theorems such as the Theorem of Pythagoras and the bisection of a chord. O The Windmill

Conditions for Congruency of Triangles Two sides and the included angle equal. (SAS) Two angles and a corresponding side equal. (AAS) Right angle, hypotenuse and side (RHS) Three sides equal. (SSS)

35 o 120 o 8 cm 10 cm 4 cm 8 cm 10 cm 8 cm 120 o 4 cm 25 o 35 o 120 o 25 o 4 cm 35 o 120 o 10 cm 8 cm 4 cm 10 cm 120 o 8 cm 35 o Not to Scale! Decide which of the triangles are congruent to the yellow triangle, giving reasons. SSS SAS AAS RHS    SAS  SSS  AAS  SAS

5 cm 12 cm 13 cm 20 o 13 cm 20 o 70 o 13 cm 12 cm 13 cm 12 cm 5 cm 13 cm 5 cm 13 cm 70 o 13 cm 70 o 20 o Decide which of the triangles are congruent to the yellow triangle, giving reasons. SSS SAS AAS RHS Not to Scale!  RHS  SSS   RHS  AAS  SAS