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In the SAS similarity criterion, the angle that must be equal in both triangles is the angle ____.

Class 10Triangles (Similarity)Geometry — Similarity
  • AIncluded between the two proportional sides
  • BOpposite the longest side
  • COpposite the shortest side
  • DEqual to 90 degrees

Step-by-Step Solution

SAS similarity requires two pairs of sides proportional and the INCLUDED angle (between those sides) equal.
Answer: A) Included between the two proportional sides

Key idea: Three similarity criteria

**AA (Angle-Angle)**: Two angles equal → similar. (Third angle is automatic by 180° angle sum.)

**SSS (Side-Side-Side proportionality)**: All three pairs of corresponding sides in same ratio → similar.

**SAS (Side-Angle-Side)**: Two pairs of sides proportional AND included angles equal → similar.

**Important**: SSA does NOT prove similarity (just like for congruence).

AA is by far the most-used in problems: spot two equal angles (often via parallel lines or shared angle) and declare similarity.

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