Question

why does a rectangle with different side lengths have only 2 lines of symmetry?
a. all four angles are congruent, and opposite sides are congruent for a horizontal and diagonal line of reflection
b. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection
c. all four angles are congruent, and opposite sides are congruent for two diagonal lines of reflection that cut through different angles
d. all four angles are congruent, and all four sides are congruent

Explanation:

Step1: Analyze line of symmetry in rectangle

A rectangle has four right - angles (all congruent). For a non - square rectangle (different side lengths), when we consider lines of reflection:
A horizontal line of reflection (mid - way between the two pairs of horizontal sides) and a vertical line of reflection (mid - way between the two pairs of vertical sides) will map the rectangle onto itself.
If we consider a diagonal line of reflection, since the adjacent sides are of different lengths, a diagonal line of reflection will not map the rectangle onto itself.

Step2: Check each option

• Option A: Diagonal line of reflection does not work for non - square rectangle.
• Option B: Correct as it mentions horizontal and vertical line of reflection.
• Option C: Incorrect description (repeated from step 1 about diagonal)
• Option D: All four sides are not congruent in a non - square rectangle

Answer:

B. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection