-ABC is an equilateral triangle-If E is the midpoint of AB and F is the midpoint of BC- which of the following statements are true-I- -AEF and -BEF are similar triangles-II- Area of quad-AEFC is 3-4 th of -ABCIII- -EBF and -ABC are similar triangles-

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Basic Proportionality Theorem

ΔABC is an eq...

Question

ΔABC is an equilateral triangle.

If E is the midpoint of AB and F is the midpoint of BC, which of the following statements are true?

I. ΔAEF and ΔBEF are similar triangles.
II. Area of (quad.)AEFC is $\frac{3}{4}^{t h}$ of ΔABC
III. ΔEBF and ΔABC are similar triangles.

Only III

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II and III

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I and III

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I, II, and III

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Solution

The correct option is B II and III

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Similar questions

Δ A B C

and

Δ E B F

Δ E B F

in sq units?

Q. ΔABC and ΔEBF are similar triangles. What is the area of ΔEBF in sq. units?

Q. In figure,

Δ A B C

is an equilateral triangle. Points

f, D

and

E

are midpoints of side

A B

, side

B C

, side

A C

respectively. Show that

Δ F E D

is an equilateral triangle.

Q. If

Δ A B C

is an isosceles triangle and midpoints

D, E,

and

F

A B, B C,

and

C A

respectively are joined, then

Δ D E F

is:

If $Δ A B C$ is an equilateral triangle and D, E and F are the midpoints of their respective sides, find the ratio of area of $Δ A B C$ to that of $Δ A D E + Δ D B F + Δ E F C .$

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ΔABC is an equilateral triangle. If E is the midpoint of AB and F is the midpoint of BC, which of the following statements are true? I. ΔAEF and ΔBEF are similar triangles. II. Area of (quad.)AEFC is 34 th of ΔABC III. ΔEBF and ΔABC are similar triangles.

The correct option is B II and III

ΔABC is an equilateral triangle.

If E is the midpoint of AB and F is the midpoint of BC, which of the following statements are true?

I. ΔAEF and ΔBEF are similar triangles.
II. Area of (quad.)AEFC is $\frac{3}{4}^{t h}$ of ΔABC
III. ΔEBF and ΔABC are similar triangles.