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Assertion (A): In the figure, if ∠EDB = ∠ACB, BE = 6 cm, EC = 4 cm and BD = 5 cm, then the length of AB is 12 cm.

Reason (R): If two triangles have two pairs of corresponding angles equal, then the triangles are similar.

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true.

  4. Both A and R are false.

In the figure, if ∠EDB = ∠ACB, BE = 6 cm, EC = 4 cm and BD = 5 cm, then the length of AB is 12 cm. Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

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Answer

In ΔEDB and ΔACB,

∠EDB = ∠ACB (Given)

∠EBD = ∠ABC [Common angles]

∴ ΔEDB ∼ ΔACB [By AA axiom]

From figure,

BC = BE + EC = 6 + 4 = 10 cm.

Since, corresponding sides of similar triangle are proportional to each other.

⇒DBCB=EBAB⇒510=6AB⇒AB=6×2⇒AB=12 cm.\Rightarrow \dfrac{DB}{CB} = \dfrac{EB}{AB} \\[1em] \Rightarrow \dfrac{5}{10} = \dfrac{6}{AB} \\[1em] \Rightarrow AB = 6 \times 2 \\[1em] \Rightarrow AB = 12 \text{ cm}.

So, Assertion (A) is true.

We know that,

If two triangles have two pairs of corresponding angles equal, then the triangles are similar, by A.A. axiom.

Reason (R) is true.

Both A and R are true.

Hence, option 3 is the correct option.

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