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Mathematics

Assertion (A): In the figure, if DE ∥ BC, then the value of x is 6 units.

Reason (R): Two similar triangles are always congruent.

  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 DE ∥ BC, then the value of x is 6 units. Similarity of Triangles, RSA Mathematics Solutions ICSE Class 10.

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Answer

Given,

DE ∥ BC,

In ΔADE and ΔABC,

∠ADE = ∠ABC (Corresponding angles are equal)

∠DAE = ∠BAC (Common angle)

∴ ΔADE ~ ΔABC

AD = 3 units

DB = 4 units

From figure,

AB = AD + DB = 3 + 4 = 7 units.

We know that,

Corresponding sides of similar triangle are proportional to each other.

⇒ADAB=DEBC⇒37=x14⇒x=3×147⇒x=6.\Rightarrow \dfrac{AD}{AB} = \dfrac{DE}{BC}\\[1em] \Rightarrow \dfrac{3}{7} = \dfrac{x}{14}\\[1em] \Rightarrow x = \dfrac{3 \times 14}{7} \\[1em] \Rightarrow x = 6.

Assertion (A) is true.

Congruent triangles must have all corresponding sides and angles equal.

Similar triangles only require corresponding angles to be equal and corresponding sides to be proportional.

Similar triangles are not always congruent.

Reason (R) is false.

A is true, R is false

Hence, option 1 is the correct option.

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