Question

are these shapes similar?
n 18 cm m
28 cm 28 cm
k 42 cm l
28 cm
s
53 cm
30 cm
p 28 cm q
yes no

Explanation:

Step1: Check Shape Types

First shape is a trapezoid (two parallel sides: \(NM = 18\) cm, \(KL = 42\) cm; non - parallel sides \(NK = ML = 28\) cm). Second shape: check sides and angles. Sides are \(RS = 28\) cm, \(RQ = 53\) cm, \(QP = 28\) cm, \(PS = 30\) cm. Angles: Let's check if corresponding angles are equal and sides are proportional.

Step2: Check Proportionality of Sides

For similar figures, corresponding sides must be in proportion. Let's list sides of first trapezoid: \(NM = 18\), \(NK = 28\), \(KL = 42\), \(ML = 28\). Second figure: \(QP = 28\), \(PS = 30\), \(RS = 28\), \(RQ = 53\). The non - parallel sides of trapezoid are 28, but in the second figure, one side is 30 and another is 53. Also, the parallel sides of trapezoid are 18 and 42, while in the second figure, the sides are 28, 28, 30, 53. The ratios of corresponding sides won't be equal. Also, the first is a trapezoid (quadrilateral with one pair of parallel sides), the second figure: let's check parallel sides. If we assume, but the side lengths don't match in proportion. For example, \(\frac{18}{28}
eq\frac{42}{53}\) and \(\frac{28}{30}
eq\frac{28}{53}\). Also, angles: the trapezoid has two pairs of adjacent equal angles (the base angles and the top angles), but the second figure's angles don't correspond. So the shapes are not similar.

Answer:

no