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Prove that, if a line is drawn parallel ...

Prove that, 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.
Using the above result, do the following:
In Fig. 7 .45 `DE abs() BC` and BD = CE. Prove that `DeltaABC` is an isosceles triangle.

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Theorem 6.1 : 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.

'If a line is drawn to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in disinct points, the other two sides are divided in the same ratio. Using this theoure. Find EC in if DE||BC.

Prove that , "If a line parallel to a side of a triangle intersects the remaining sides in two distinct points then the line divides the sides in the same proportion".

Basic proportionality Theorem or Thales Theorem - If a line is drawn parallel to one side of a triangle intersecting the other two sides; then it divides the two sides in the same ratio.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral, so formed is cyclic.

Prove that a line drawn from the vertex of a triangle to its base is bisected by the line joining the mid points of the remaining two sides of the triangle.

The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.

VK GLOBAL PUBLICATION-TRIANGLES-LONG ANSWER QUESTIONS
  1. The line drawn from the midpoint of one side of a triangle parallel to...

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  2. ABCD is a trapezium in which AB||DC and its diagonals intersect each ...

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  3. If AD and PM are medians of triangles ABC and PQR, respectively where...

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  4. In Fig. 4.123, ABCD is a trapezium with AB || DC. If Delta AED is sim...

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  5. Prove that the area of an equilateral triangle described on a side of ...

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  6. If the areas of two similar triangles are equal, prove that they ar...

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  7. The areas of the two similar triangles are in the ratio of the square ...

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  8. O is the a point in the interior of Delta ABC, OD bot BC, OE bot AC an...

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  9. The perpendicular from A on side BC of a ABC intersects BC at D such t...

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  10. In an equilateral triangle, prove that three times the square of on...

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  11. Prove that, if a line is drawn parallel to one side of a triangle to i...

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  12. In DeltaABC A = 90^@ and AC | BD, then Show that (a) AB^2=BC.BD (b) A...

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  13. Diagonals of a trapezium ABCD with AB || DC intersect each other at...

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  14. Prove that, in a right triangle, the square of the hypotenuse is equal...

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  15. In a triangle, if the square on one side is equal to the sum of the sq...

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  16. ABC is a triangle in which AB = AC and D is a point on AC such that ...

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  17. Prove that the area of an equilateral triangle described on one sid...

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  18. D and E are points on the sides CA and CB respectively of a triangle ...

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