Chapter 6 · Question 4

State the SSS and SAS similarity criteria.

Answer

Direct Answer

SSS: If corresponding sides of two triangles are proportional, the triangles are similar. SAS: If one angle is equal and the corresponding sides including that equal angle are proportional, the triangles are similar.

Simple Explanation

SSS uses all three side ratios. SAS uses two side ratios and the included angle.

Exam-Ready Structure

For SSS similarity, if

\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CA}{RP}

, then

\triangle ABC\sim\triangle PQR

. For SAS similarity, if

\angle A=\angle P

and

\frac{AB}{PQ}=\frac{AC}{PR}

, then the triangles are similar.

Key Points

SSS: If corresponding sides of two triangles are proportional, the triangles are similar.