NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.1
Question 7

Question.  7

7. In triangles \(ABC\) and \(DEF\), if \(\angle B=\angle E\), \(\angle F=\angle C\) and \(AB=3\,DE\), the triangles are

(A)

congruent but not similar

(B)

similar but not congruent

(C)

neither

(D)

congruent as well as similar

Detailed Answer with Explanation:

Step 1: We are told that \(\angle B = \angle E\) and \(\angle F = \angle C\).

This means two angles of triangle \(ABC\) are equal to two angles of triangle \(DEF\).

Step 2: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar by the AA (Angle–Angle) similarity rule.

Step 3: To be congruent, all sides of the two triangles must be exactly the same length (or have the same ratio of 1:1).

But here, \(AB = 3 \times DE\). So the ratio of sides is \(3:1\), not \(1:1\).

Step 4: Therefore, the triangles are similar (because of equal angles), but not congruent (because the sides are not equal in length).

Final Answer: Similar but not congruent.

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 6: Triangles – Exercise 6.1 | Detailed Answers