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2.23 Properties of Similar Triangles

Congruency and Similarity: Figures that have same shape and size are said to be congruent, whereas figures need to be of the same shape but not necessarily of the same size for them to be similar.

Properties of similar triangles
Property 1: If in two triangles, angles are equal, then their corresponding sides are proportional and hence the triangles are similar. This property is called AAA postulate.
Property 2: If one angle of two triangle is equal to the other and their sides are proportional, then the triangles are similar by SAS postulate.
Property 3: If two angles and one side of two triangles are equal, then they are similar by ASA postulate.

Example: In triangle ABC, prove that ABC and DEF are similar.

Solution:: In triangles ABC and ADE, we have
angle A = angle A (common angle)
angle B = angle E (90o)
Hence triangles ABC and ADE are similar.

Directions: Solve the following problems. Also write at least 5 examples of your own.

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2.23 Properties of Similar Triangles

Q 1: Given two triangles ABC and DEF. AB = 3 cms, angle A = 40, angle D = 40, AC = 5 cms, DE= 4.5 cm, find angle B DF = 7.5 cm

Q 2: Find angle EBA.


Q 3: The perimeters of two similar triangles are 30 and 20 respectively. If one side of the first triangle is 12, determine the corresponding side of the other triangle.
12 cm
15 cm
8 cm

Q 4: State if the given pair of triangles are congruent and the criterion used?


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