Question

row 4
two rectangles are always similar.
true
false
row 5
two regular octagons are always similar.
true
false

Explanation:

Step1: Analyze Row 4 (Two rectangles are ALWAYS similar)

A rectangle has four right angles, but the side lengths can vary. For two rectangles to be similar, their corresponding sides must be in proportion. For example, a rectangle with length 2 and width 1, and another with length 3 and width 2: the ratios are \( \frac{2}{3} \) and \( \frac{1}{2} \), which are not equal. So two rectangles are not always similar. So the correct answer for Row 4 is False.

Step2: Analyze Row 5 (Two regular octagons are ALWAYS similar)

A regular octagon has all sides equal and all interior angles equal (each interior angle of a regular octagon is \( 135^\circ \)). By the definition of similar polygons, if two polygons are regular and have the same number of sides, their corresponding angles are equal and their corresponding sides are in proportion (since all sides of each regular octagon are equal, the ratio of corresponding sides will be constant). So two regular octagons are always similar. So the correct answer for Row 5 is True.

Answer:

Row 4: False
Row 5: True