Question Video: Verifying Whether Two Given Polygons Are Similar Mathematics

Video Transcript

Are the two polygons similar?

Two polygons are similar if the corresponding angles are equal in measure and their corresponding side lengths are proportional. So we need to find the measure of angle 𝐴 and the measure of angle 𝐸. Each polygon should have all of the angles adding up to be 360 degrees. So to find the measure of angle 𝐴, we need to take 360 degrees and then subtract all of the three angles we already know, and then the remainder will be left for angle 𝐴. So we’re subtracting 103 degrees, 84 degrees, and 95 degrees. So the measure of angle 𝐴 is 78 degrees.

Now, in the other polygon, the measure of angle 𝐸, we would do the exact same thing. So after subtracting the three angles from 360, we get 95 degrees. So the measure of angle 𝐴 is equal to the measure of angle 𝐹, so they’re both 78 degrees. Angle 𝐵 and angle 𝐺 are both 103 degrees, angle 𝐶 and angle 𝐻 are both 84 degrees, and then lastly angle 𝐷 and angle 𝐸 are both 95 degrees. This means our corresponding angles are equal in measure.

Now, let’s check if the side lengths are proportional. 𝐴𝐵 to 𝐹𝐺 is 20 to 14, 𝐵𝐶 to 𝐺𝐻 is just 16 to 11, 𝐶𝐷 to 𝐻𝐸 is 20 to 14, and 𝐷𝐴 to 𝐸𝐹 is 18.6 to 13. So we need to check if each of these fractions are proportional; do they reduce to be the exact same number? Unfortunately, they are not. These fractions do not reduce to be the exact same fraction; they’re not proportional. Since the side lengths are not proportional, the polygons are not geometrically similar.