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Properties of Parallelograms

ABC is a tria...

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ABC is a triangle in which DE\vert\vert BCsuch that AD/DB=3/2.Prove that △ DEF∼△ CBF and also find the ratio ar(△ DEF):ar(△ DEC),where F is the point of intersection of DC and BE

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Q. In the given figure, ABC is a triangle, DE is parallel to BC and

\frac{A D}{D B} = \frac{3}{2}

i) Determine the ratios

\frac{A D}{A B}, \frac{D E}{B C}

Δ D E F

Δ C B F

\frac{E F}{F B}

iii) What is the ratio of the areas of

Δ D E F

Δ B F C

Q. In ∆ABC, AD and BE are altitude. Prove that

\frac{ar (∆ DEC)}{ar (∆ ABC)} = \frac{{DC}^{2}}{{AC}^{2}}

D, E, F

are the mid-points of the sides

B C, C A

A B

respectively of

△ A B C

B D E F

is a parallelogram. And also show that

a r (△ D E F) = \frac{1}{4} a r (△ A B C)

Q. If D is a point on the side AB of

△

ABC such that AD : DB = 3:2 and E is a point on BC such that DE

∥

AC. Find the ratio of areas of

△

△

Q. D, E, and F are, respectively the mid-points of sides BC, CA and AB of an equilateral triangle ABC. Prove that DEF is also an equilateral triangle.

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Properties of Parallelograms

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