Institute: Central Board of Secondary Education (CBSE)

Subject: Mathematics

Topic: Geometry - Triangles

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#### shaalaa.com | Triangles part 1 (Similar Figures)

#### Series 1: playing of 46

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Triangles

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Triangles part 1 (Similar Figures)

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Triangles part 2 (Example Similar Figures)

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Triangles part 3 (Thales theorem Activity)

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Triangles part 4 (Thales theorem Proof)

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Triangles part 5 (Converse of Thales theorem)

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Triangles part 6 (Example Thales theorem)

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Triangles part 7 (Example Thales theorem)

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Triangles part 8 (Example Thales theorem)

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Triangles part 9 (Example Thales theorem)

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Triangles part 10 (Internal Bisector Theorem)

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Triangles part 11 (Converse Internal Bisector Theorem)

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Triangles part 12 (External Angle Bisector)

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Triangles part 13 (Examples Angle Bisector)

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Triangles part 14 (Examples Angle Bisector)

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Triangles part 15 (Examples Angle Bisector)

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Triangles part 16 (Examples Angle Bisector)

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Triangles part 17 (Examples Angle Bisector)

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Triangles part 18 (AAA Angle Angle Angle Similarity)

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Triangles part 19 (SSS Side Side Side Similarity)

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Triangles part 20 (SAS Side Angle Side Similarity)

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Triangles part 21 (Examples Similarity of triangle)

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Triangles part 22 (Examples Similarity of triangle)

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Triangles part 23 (Examples Similarity of triangle)

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Triangles part 24 (Examples Similarity of triangle)

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Triangles part 25 (Examples Similarity of triangle)

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Triangles part 26 (Examples Similarity of triangle)

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Triangles part 27 (Examples Similarity of triangle)

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Triangles part 28 (Examples Similarity of triangle)

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Triangles part 29 (Examples Similarity of triangle)

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Triangles part 30 (Examples Similarity of triangle)

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Triangles part 31 (Examples Similarity of triangle)

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Triangles part 32 (Examples Similarity of triangle)

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Triangles part 33 (Examples Similarity of triangle)

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Triangles part 34 (Examples Similarity of triangle)

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Triangles part 35 (Theorem Ratio of Sides of triangle)

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Triangles part 36 (Theorem Ratio of Area of triangle)

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Triangles part 37 (Example Ratio of Area of triangle)

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Triangles part 38 (Proof Pythagoras Theorem)

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Triangles part 39 (Proof Converse of Pythagoras Theorem)

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Triangles part 40 (Acute and Obtuse angle theorem Proof)

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Triangles part 41 (Example Pythagoras Theorem)

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Triangles part 42 (Example Pythagoras Theorem)

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Triangles part 43 (Example)

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Triangles part 44 (Example Pythagoras Theorem)

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Triangles part 45 (Example Pythagoras Theorem)

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Triangles part 46 (Example and Summary)

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Definitions, examples, counter examples of similar triangles.

- (Prove) 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.
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
- (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
- (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle.