2. Introduction
• • Congruent figures: same shape and size.
• • Similar figures: same shape, not necessarily the same size.
• • Chapter focus: Similarity of triangles, indirect measurement, Pythagoras
theorem.
3. Definition of Similar Figures
• • All circles are similar.
• • All squares and all equilateral triangles are similar.
• • Two polygons are similar if:
• (i) Corresponding angles are equal
• (ii) Corresponding sides are in same ratio
4. Similarity of Triangles
• • A triangle is also a polygon.
• • Two triangles are similar if:
• (i) Corresponding angles are equal
• (ii) Corresponding sides are in same ratio
5. Basic Proportionality Theorem
(Thales Theorem)
• • If a line is drawn parallel to one side of a triangle, it divides the other
two sides in the same ratio.
• • Converse: If a line divides any two sides of triangle in same ratio, it is
parallel to third side.
6. Criteria for Similar Triangles
• • AAA: All three corresponding angles are equal
• • AA: Two corresponding angles are equal (third is automatically equal)
• • SSS: Sides in same ratio → angles are equal → triangles are similar
• • SAS: One angle equal + included sides in same ratio → triangles are
similar
7. Solved Examples
• • Proving similarity using criteria (AA, SSS, SAS).
• • Real-life application: shadow length problem using triangle similarity.
• • Using medians, altitudes, or diagonals to prove similarity.
8. Classroom Activities
• • Activity 1: Create shadows with cut-outs (shape projection).
• • Activity 2: Use triangles on graph paper to explore similarity.
• • Activity 3: Use line segments & parallel lines to verify theorems.
9. Summary
• • Similar figures → same shape, not size.
• • Triangles have 4 similarity criteria: AA, AAA, SSS, SAS.
• • Used in real-world calculations like heights, distances.
• • Proportionality theorem is key to triangle similarity.
