Question

are these shapes similar?
left trapezoid: c to d is 25 ft, d to e is 27 ft, e to f is 43 ft, f to c is 27 ft. angles at c, d, f, e are marked. right quadrilateral: k to l is 24 ft, l to i is 26 ft, i to j is 24 ft, j to k is 43 ft. angles at k, l, i, j are marked. options: yes, no

Explanation:

Step1: Check corresponding sides' ratios

First, identify corresponding sides. For the trapezoid (CDEF) and the quadrilateral (KLIJ), check the ratios of sides:

• Side CD (25 ft) vs IJ (24 ft): $\frac{25}{24}\approx1.04$
• Side DE (27 ft) vs KL (24 ft): $\frac{27}{24}=1.125$
• Side EF (43 ft) vs KJ (43 ft): $\frac{43}{43}=1$
• Side FC (27 ft) vs LI (26 ft): $\frac{27}{26}\approx1.038$

Step2: Analyze angle and side consistency

Similar figures require corresponding angles equal and corresponding sides in proportion. Here, the side ratios are not equal (e.g., 25/24 ≠ 27/24, 27/26 ≠ 1, etc.). Also, the first figure is a trapezoid (with two parallel sides, CD and EF, since legs are equal, it's isosceles trapezoid) and the second is a quadrilateral with sides 24, 43, 24, 26 – the side lengths don't match the proportion needed for similarity.

Answer:

no