Two tests, both required
Similar polygons: corresponding angles congruent, and corresponding sides proportional. One constant ratio for every pair of matching sides. That ratio is the scale factor.
Write the similarity statement so the letters already match: ABCD ~ EFGH means A↔E, B↔F, C↔G, D↔H, so AB matches EF, BC matches FG, ∠D matches ∠H.
A dilation produces similar polygons. Stretching only the base and not the height would wreck the third side, so a true dilation scales every length by the same k.
Check a proportion
Rectangle 25 by 5 next to rectangle 15 by 3. Test 25/15 ? 5/3. Cross multiply: 25·3 = 75 and 15·5 = 75. Equal products, so the ratios match, so the rectangles are similar. Or reduce 25/15 to 5/3 and see it already matches.
Missing length: trapezoids similar, AD = 12 matches EH = x, BC = 4 matches FG = 2. Then 12/x = 4/2. Cross multiply: 24 = 4x, x = 6.
Angles come along
Once the polygons are similar, every matching angle pair is congruent, even the ones with no mark. That is the other half of the definition, not a bonus.
You can slide a small triangle onto the corner of a larger similar one to see the angles sit on each other. The course does that after a dilation of 2: base 3 becomes 6, height 4 becomes 8, then a translation lines up an angle to check it.