Question

ΔАВC is reflected in origin to get ΔΑ'Β'C'.

Statement (1): ΔABC is congruent to ΔΑ'Β'C'. 

Statement (2): The two triangles are similar to each other.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

When a point (x, y) is reflected across the origin, its image becomes (−x, −y).

So, under this transformation:

• All angles and side lengths are preserved.

• The orientation (clockwise/counter-clockwise) is reversed, but the size and shape remain identical.

According to statement 1: Δ ABC is congruent to Δ A'B'C' because in reflection lengths and angles are preserved.

So, statement 1 is true.

According to statement 2: Δ ABC is similar to Δ A'B'C' because all congruent triangles are similar.

So, statement 2 is true.