Question

are the polygons below similar?

(image of two polygons: left polygon tqrs with sides tq=16, qr=16, rs=16, st=16; angles at q and s are 140°, angles at t and r are marked with red arcs. right polygon gjih with sides gj=20, ji=20, ih=20, hg=20; angles at g and i are 43°, angles at j and h are marked with red arcs. below the polygons, options: yes, no)

Explanation:

Step1: Check Angle Conditions

For similar polygons, corresponding angles must be equal. In the first polygon (TQRS), the angles at T and R are equal (marked), and angles at Q and S are \(140^\circ\). The sum of interior angles in a quadrilateral is \(360^\circ\), so the unmarked angles (at T and R) can be calculated: \( \frac{360 - 140 - 140}{2}= 40^\circ\). In the second polygon (GHIJ), the marked angles are \(43^\circ\), so corresponding angles are not equal (\(40^\circ
eq 43^\circ\)).

Step2: Check Side Proportions

First polygon has all sides \(16\) (so ratio of sides is \(1\)). Second polygon has all sides \(20\) (ratio of sides is \(1\)). But since angles don't match, similarity fails.

Answer:

no