Introduction To Similar Triangles

Similar Triangles Introduction Geometrical figures which are of the same shape and same size are known as congruent figures, but figures which are of the same shape but not necessarily of the same size are known as similar figures. Two congruent figures are always similar, but two similar figures may not be congruent. If we make different sizes of photographs from the same negative, they all look alike in shape thought their sizes are different.

Similar Triangles Two triangles are said to be similar to each other if: a. their corresponding angles are equal. b. their corresponding sides are proportional. is similar AB BC CA = = ∠A = ∠P, ∠B = ∠Q and ∠C = ∠R and PQ QR RP

In

figure

6-1,

if

Triangle ABC

to

Triangle PQR ,

then

When two triangles Triangle ABC and Triangle PQR are similar, we writeTriangle ABC Similar to Triangle PQR . Here, the order of letters play very important part. For example, if we write

Triangle DEF Similar to Triangle GHK , it means ∠F = ∠K and DE EF FD . This should be noted very carefully. = = GH HK KG

∠D = ∠G, ∠E = ∠H and

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