Question

What are similar triangles?

Answer 1

Definition of Similar triangles.

Similar triangles are triangles that have the same shape, but their sizes may vary.

Any two triangles of the same shape are said to be similar if they have equal pair of corresponding angles and the equal pair of corresponding sides in the same proportion. That is for any two triangles $ABC$ and $PQR$,

$\frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$

Characteristics of similar triangles are:

• $AAA$(Angle Angle Angle ): All three pairs of corresponding angles are the same
• $SSS$(Side Side Side): All three pairs of corresponding sides are the same
• $SAS$(Side Angle Side):Two pairs of corresponding sides and included angle equal.

Thus, any two triangles of the same shape are said to be similar if they have equal pair of corresponding angles and an equal pair of corresponding sides.