Class 10 Maths Chapter 6, Triangles, shifts from congruence (studied in Class 9) to similarity of figures, proves the Basic Proportionality Theorem (Thales’s Theorem) and its converse, and establishes the AAA,AA, SSS and SAS criteria for similarity of triangles.
What Class 10 Mathematics (Ganit — Hindi Medium) Chapter 6 Covers
6.1 & 6.2 Similar Figures & Similarity of Triangles (Thales’s Theorem) defines similarity of polygons (equal corresponding angles and proportional corresponding sides), proves Theorem 6.1 (Basic Proportionality Theorem / Thales’s Theorem: if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio, AD/DB = AE/EC) and Theorem 6.2 (its converse), and applies them to trapezium diagonals.
6.3 Criteria for Similarity of Triangles proves and applies the AAA (and AA) similarity criterion (Theorem 6.3), the SSS similarity criterion (Theorem 6.4) and the SAS similarity criterion (Theorem 6.5).
Exercises in Chapter 6
- Exercise 6.1 (3 Questions) distinguishes similar figures from congruent figures.
- Exercise 6.2 (10 Questions) applies the Basic Proportionality Theorem and its converse to parallel lines inside triangles and the diagonals of a trapezium.
- Exercise 6.3 (16 Questions) uses AA, SSS and SAS similarity criteria on intersecting chords, altitudes, medians, angle bisectors and vertical pole shadow problems.
Read Class 10 Mathematics (Ganit — Hindi Medium) Chapter 6 Online
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FAQ
State the Basic Proportionality Theorem (Thales’s Theorem).
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio (i.e., if DE \parallel BC in △ ABC, then AD/DB = AE/EC).
What are the three main criteria for similarity of two triangles?
(1) AA (or AAA) similarity: two angles of one triangle are respectively equal to two angles of the other; (2) SSS similarity: all three pairs of corresponding sides are in the same ratio; (3) SAS similarity: one angle of a triangle is equal to one angle of the other and the sides including these angles are proportional.