NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Multiple Choice Questions
Question 15

Question.  15

The number of lines of symmetry in a 45°–45°–90° set-square is

(A)

0

(B)

1

(C)

2

(D)

3

Detailed Answer with Explanation:

Beginner-Friendly Explanation (Step by Step)

Shape: A 45°–45°–90° set-square is an isosceles right triangle.

  1. In this triangle, two angles are equal:

    (45^circ) and (45^circ).

  2. Because the two angles are equal, the two sides opposite them are also equal:

    Let the equal sides be (AB) and (AC).

    So, (AB = AC).

  3. A line of symmetry is a line that folds the shape into two matching halves.

    For an isosceles triangle, this line goes from the vertex between the equal sides to the midpoint of the base.

  4. Here, the vertex between the equal sides is the right-angle vertex.

    Draw a line from the right-angle vertex to the midpoint of the hypotenuse.

    This line is the angle bisector of (90^circ):

    It splits (90^circ) into (45^circ) and (45^circ).

    It is also the perpendicular bisector of the hypotenuse.

  5. This single line makes the two halves exactly the same.

    So, there is one line of symmetry.

Answer: (1) line of symmetry. (Option B)

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