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State true or false.

In the following figure, $C D | | A E$ and $C Y | | B A$ and . Then $a r Δ B C Y Z = a r Δ E D Z$ . Then .

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True

False

answer is A.

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Detailed Solution

Given that,

C D | | A E

and

C Y | | B A

Evaluate,

Δ A C E

and

Δ A D E

are on the same base

A E

and between the same parallels.

C D ‖ A E .

We know that the area on the same base and between the same parallels are equal in area. So,
Area

(Δ A C E) =

Area

(Δ A D E)

Area

(Δ C E A) −

Area

(Δ A Z E) =

Area

(Δ A D E) − A r (Δ A Z E)

Area

(Δ C Z A) =

Area

(Δ Z D E)

……(1)
Evaluate,

Δ C B Y

and

Δ C A Y

are on the same base

and between the same parallels.

C Y ‖ B A .

Then, area

(Δ C B Y) =

Area

(Δ C A Y)

Add

Δ C Y G

on both sides,
Analyse that,
Area

(Δ C B Y) +

Area

(Δ C Y G) =

Area

(Δ C A Y) +

Area

(Δ C Y G)

Area

(B C Y Z) =

Area

(Δ C Z A)

……(2)
Compare (1) and (2),
Area

(B C Z Y) =

Area

(Δ E D Z)

Hence, the statement is true.
Therefore, option 1 is correct.

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State true or false.In the following figure, CD||AE and CY||BA and . Then ar ΔBCYZ = ar ΔEDZ . Then .

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State true or false.

In the following figure, $C D | | A E$ and $C Y | | B A$ and . Then $a r Δ B C Y Z = a r Δ E D Z$ . Then .