Question

are the polygons below similar?
(image of two quadrilaterals: left labeled e, d, c, b with sides ed=24, dc=16, cb=12, be=16; right labeled r, q, p, s with sides rq=6, qp=4, ps=3, sr=4. angles marked for similarity check. below: radio buttons yes, no, submit button, work it out text)

Explanation:

Step1: Check Corresponding Angles

The marked angles (congruent arc marks) suggest that corresponding angles are equal. So angle - angle similarity condition (AA) is partially checked via marked angles.

Step2: Check Corresponding Sides Ratio

For the first quadrilateral (EBCD) and the second (RQPS), we check the ratios of corresponding sides.

• Ratio of \( ED = 24\) and \( RQ=6\): \(\frac{24}{6} = 4\)
• Ratio of \( DC = 16\) and \( QP = 4\): \(\frac{16}{4}=4\)
• Ratio of \( CB=12\) and \( PS = 3\): \(\frac{12}{3}=4\)
• Ratio of \( BE = 16\) and \( SR = 4\): \(\frac{16}{4}=4\)

Since all corresponding sides are in proportion (ratio = 4) and corresponding angles are equal (from marked arcs), the polygons are similar.

Answer:

yes