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A triangle has sides 10 cm, 24 cm and 26 cm. Every side is now multiplied by 1.5. The new triangle is ____.

Class 10Triangles (Similarity)Geometry — Similarity
  • Aright-angled and similar to the original
  • Bright-angled but not similar to the original
  • Cno longer right-angled
  • Dobtuse-angled

Step-by-Step Solution

The original is right-angled since . The new sides 15, 36, 39 satisfy , so it is still right-angled. Multiplying all three sides by the same factor makes the triangles similar by SSS, and similar triangles have equal angles — so the shape, and the right angle, cannot change.
Answer: A) right-angled and similar to the original

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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