Question

1. which pair of polygons is similar?

a.
triangle with legs 5, 12, hypotenuse 13 right triangle with legs 4, 3, hypotenuse 5

b.
square with side 4 rhombus with side 4

c.
rectangle with length 5, width 1 rectangle with length 10, width 2

d.
isosceles triangle with equal sides 10, base 6 isosceles triangle with equal sides 5, base 6

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Explanation:

Step1: Recall Similar Polygon Rules

Similar polygons have equal corresponding angles and proportional corresponding sides.

Step2: Analyze Option A

Left triangle: sides \(5, 12, 13\) (right triangle). Right triangle: sides \(3, 4, 5\) (right triangle). Check ratios: \(\frac{5}{5}=1\), \(\frac{12}{4}=3\), \(\frac{13}{3}\approx4.33\). Ratios not equal. Not similar.

Step3: Analyze Option B

Left: square (all sides \(4\), angles \(90^\circ\)). Right: rhombus (all sides \(4\), but angles may not be \(90^\circ\)). Angles not equal. Not similar.

Step4: Analyze Option C

Left rectangle: length \(5\), width \(1\). Ratios: \(\frac{\text{length}}{\text{width}}=\frac{5}{1}=5\). Right rectangle: length \(10\), width \(2\). Ratio: \(\frac{10}{2}=5\). Corresponding angles are \(90^\circ\) (equal). Sides proportional (\(\frac{5}{10}=\frac{1}{2}\), \(\frac{1}{2}=\frac{1}{2}\)). Similar.

Step5: Analyze Option D

Left isosceles triangle: sides \(10, 10, 6\). Right: sides \(5, 5, 6\). Ratios: \(\frac{10}{5}=2\), \(\frac{6}{6}=1\). Ratios not equal. Not similar.

Answer:

C. The pair of rectangles in option C (with dimensions 5×1 and 10×2) are similar because their corresponding angles are equal (all 90°) and their corresponding sides are proportional (5/10 = 1/2 and 1/2 = 1/2).