State whether given statement is true or false
If two triangles with the same base have equal area, then prove that they lie between the same parallel lines.

True

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False

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Solution

The correct option is A True
Area $(△ E C B) =$ Area $(△ G C D)$
$\frac{1}{2} | B C | | D R | = \frac{1}{2} | B C | | E G |$
$| D F = | E G |$
Also $E G ⊥ B C$ & $D F ⊥ B C$
then
$D$ & $E$ are equidistant fro $B C$
and $P E ∥ B C$ because line joining equidistant point from a line is $11$ to that line

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Similar questions

Two triangles having the same base (or equal bases) and equal areas need not necessarily lie between the same parallels.

Question 67

State whether the statement is True or False.

Triangles having the same base have equal area.

Prove that two triangles on the same base (or equal bases) and between the same parallels are equal in area.
[4 MARKS]

Choose the correct statements from the following:

Statement 1: All the parallelograms having the same base and lying between the same parallels have equal areas.

Statement 2: All the parallelograms having the same base and lying between the same parallels have same perimeters.

Statement 3: Of all the parallelograms having same base and lying between same parallels, rectangle will have the smallest perimeter.

Statement 4: All the parallelograms having equal areas must have the same base but they may or may not lie between the same parallels.

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