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Theorem 6.1 : If a line is drawn paralle...

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.

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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.

'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.

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.

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".

(B) Solve any two of the following subquestions : Prove that following statement, " If a line parallel to a side of a Delta intersects the remaining sides in two distinct points , then the line divides the sides in the same proportion . "

Thales theorem is given by a greek mathematician. According to this theorem, if a line is drawn parallel to one side of a triangle then it divides the other two sides in the same ratio. This theorem is also known as Basic Proportionality Theorem. Here, the value of x is :

Theorem 6.2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 8.10 : The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

CBSE COMPLEMENTARY MATERIAL-TRIANGLE-Short Answer Type Questions-II
  1. Theorem 6.1 : If a line is drawn parallel to one side of a triangle to...

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  2. In the given figure, (QR)/(QS)= (QT)/(PR) and angle1 = angle2 then pro...

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  3. In equilateral triangleABC, ADbotBC. Prove that 3BC^2= 4AD^2.

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  4. In the given figure angleABC=90^(@) and CD bot AB. Prove that (BC^(2)...

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  5. In Fig. 4.179, A B C and D B C are on the same base B C . If A...

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  6. If AD and PS are medians of triangleABC and trianglePQR respectively w...

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  7. In the given figure, DE || AC. Which of the following is correct? x=(...

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  8. Prove that the sum of the squares of the sides of a rhombus is equa...

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  9. A street light bulb is fixed on a pole 6 m above the level of the stre...

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  10. Two poles of height a metres and b metres are p metres apart. Prove th...

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  11. In the given figure AB || PQ || CD, AB=x, CD=y and PQ=z. Prove that 1/...

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  12. In the given figure (PS)/(SQ)=(PT)/(TR) and anglePST = anglePRQ. Prove...

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  13. In the figure, a point O inside triangleABC is joined to its vertices....

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  14. Two triangles B A Ca n dB D C , right angled at Aa n dD respectively, ...

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  15. The Hypotenuse of a right triangle is 25 cm and out of the remaining t...

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  16. In the given figure DE || AC and (BE)/(EC)=(BC)/(CP). Prove that DC |...

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  17. In a quadrilateral ABCD, angleB=90^(@) and AD^(2)= AB^(2) + BC^(2)+CD^...

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  18. In the given figure, DE || BC, DE= 3 cm, BC = 9 cm and ar (DADE) = 30c...

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  19. In an equilateral triangle ABC, D is a point on side BC such that B D=...

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  20. Ii DeltaPQR, PDbotQR such that D lies on QR, if PQ=a,PR=b,QD=c and DR=...

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  21. The ratio of the the areas of two similar triangles is equal to the ra...

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