# Euclidean Geometry Revision Similar triangles Similar triangles are

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Euclidean Geometry Revision

Similar triangles � Similar triangles are triangles that have the same shape but not necessarily the same size.

Two triangles are similar if: � All three pairs of corresponding angles are equal. � y n m x z o y i j x z k

Note…. . � We use the symbol III to indicate similarity. � When proving triangles that are similar the reason for similarity is always angle, angle (AAA)

Example � L O * M * N P Q

Example 1. Prove that triangles ABD and ACD are similar. A 1 2 B 1 2 D C

2. Determine the lengths of the unknown sides in the triangle below. A x 1 5 E 2 2 B 1 2 C 3 2. 5 y D

Congruency �

The four conditions of congruent triangles: Condition 1: Side (SSS) � If triangles have three sides that are equal, the triangles are congruent. Condition 2: Side Angle Side (SAS) � If triangles have two sides and an included angle that are equal, the triangles are congruent.

Condition 3: Angle Side (AAS) � If triangles have two angles and a single corresponding side that are equal, the triangles are congruent. Condition 4: Right-angle Hypotenuse Side (RHS) � If the hypotenuse and one other side are equal in right angled triangles, the triangles are congruent.

Example 1. B Determine the length of x in the triangle A below. 30º x 1 2 D 5 C

� A D B C