Mathematics
The perpendicular BD drawn from the vertex of a right triangle ABC.
Assertion (A) : Triangles ABD and BCD are similar to each other.
Reason (R) : Triangles, which are similar to the same triangle, are similar to each other.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
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Answer
In Δ ABC and Δ ABD,
⇒ ∠ABC = ∠ADB (Both are 90°)
⇒ ∠BAC = ∠BAD (Common angle)
∴ Δ ABC ∼ Δ ADB (By AA postulate) ………. (1)
Similarly, in Δ ABC and Δ BDC,
⇒ ∠ABC = ∠BDC (Both are 90°)
⇒ ∠BCA = ∠BCD (Common angles)
∴ Δ ABC ∼ Δ BDC (By AA postulate) ………. (2)
As,
Triangles, which are similar to the same triangle, are similar to each other.
From equation (1) and (2), we get :
Δ ADB ∼ Δ BDC
∴ Both A and R are true and R is correct reason for A.
Hence, option 3 is the correct option.
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