Real Numbers

12 Topics | 4 Quizzes
Polynomials

13 Topics | 4 Quizzes
Pair of Linear Equations in Two Variables

4 Topics | 4 Quizzes
Quadratic Equations

7 Topics | 4 Quizzes
Arithmetic Progressions

5 Topics | 4 Quizzes
Triangles

8 Topics | 4 Quizzes
Coordinate Geometry

9 Topics | 4 Quizzes
Introduction to Trigonometry

7 Topics | 4 Quizzes
Some Applications of Trigonometry

5 Topics | 2 Quizzes
Circles

5 Topics | 2 Quizzes
Constructions

3 Topics | 2 Quizzes
Areas Related to Circles

5 Topics | 3 Quizzes
Surface Areas and Volumes

4 Topics | 2 Quizzes
Statistics

8 Topics | 2 Quizzes
Probability

4 Topics | 1 Quiz
It is the opposite of basic proportionality theorem, which says that if in a given Triangle a straight line divides the two sides of the Triangle in the same ratio then that straight line is parallel to the third side of the Triangle.

**Theorem 2:**

If a line divides any of the two sides of a triangle in the same ratio, then that line is parallel to the third side.

ABC is a triangle in which DE divides AC and AB in the same ratio. This states that:

AB/DB = AE/EC

Construction: Draw a line DE’ from point D to E’ at AC. Let us consider DE’||BC.

**Proof:**

To prove: If DE` || BC, then

AB/DB = AE`/E`C

According to the theorem, AB/DB = AE/EC

Then, accordingly, E and E` must be coincident.

This proves that DE || BC

Proved.

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