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Q.

In the given figure, DEFG is a square and $∠$ BAC=90° State if the condition

${DE}^{2} = BD \times EC$ , is true or false.

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a

True

b

False

answer is A.

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Detailed Solution

It is given that, DEFG is a square and ∠BAC=

90^{°} .

Question Image

We can write that,
In ΔAFG and ΔDB
∠GAF=∠BDG
∠AGF=∠DBG (corresponding angles because GF|| BC and AB are the transversal )
ΔAFG≈ΔDBG (by AA Similarity Criterion)
In ΔAGF&ΔEFC
∠AFG=∠CEF
∠AFG=∠ECF (corresponding angles because GF|| BC and AC is the transversal)
ΔAFG≈ΔEFC (by AA similarity criterion)
The ratio of the corresponding sides of similar triangles are equal.
Hence, we can write that,

\frac{BD}{EF} = \frac{DG}{EC}

\frac{BD}{DE} = \frac{DE}{EC}

{DE}^{2} = BD \times EC

Therefore, the given statement is true i.e.,

{DE}^{2} = BD \times EC

.
Hence, the correct option is 1.

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