### Video Transcript

Are these two polygons similar? If yes, find the scale factor from polygon ππππΏ to polygon π΄π΅πΆπ·.

So weβre asked to determine whether the two quadrilaterals are similar. Letβs recall the criteria that are necessary for two polygons to be similar. Firstly, itβs necessary that corresponding angles in the two polygons are congruent. Secondly, itβs necessary that corresponding side lengths are proportional. Weβll take each of these statements in turn, beginning with the angles.

We can see from the way the diagram has been marked that three of the angles in the two polygons are indeed congruent. The final angle must also be congruent, as the angle sum in a quadrilateral is always 360 degrees. Therefore, the first condition for similarity is fulfilled. Corresponding angles between the two polygons are indeed congruent.

Now letβs consider the proportionality of the corresponding side lengths. Pairs of corresponding sides have now been marked in the same color. And so we need to determine whether itβs true that the ratio between these pairs of sides is constant for all four pairs. Weβll begin with π·πΆ divided by πΏπ which is 2.56 divided by 3.2. This simplifies to just 0.8.

What we now want to determine is whether the three remaining pairs of sides give the same ratio. The measurements for πΆπ΅ and ππ are in fact the same as the measurements for π·πΆ and πΏπ. So we can conclude straightaway that they will give the same ratio. We need to look at the other two pairs of sides. The ratio of π΅π΄ to ππ is 3.84 divided by 4.8. This also simplifies to 0.8.

So far, we have three pairs of corresponding side lengths which are proportional, with a scale factor of 0.8. We need to check the final pair. π΄π· divided by ππΏ is 2.72 divided by 3.4. And this ratio does also simplify to 0.8. So as all four pairs of corresponding sides have the same scale factor of 0.8, we can conclude that corresponding side lengths are indeed proportional. And therefore, the second criteria for similarity is also fulfilled.

So our answer to the problem then is that yes, the two polygons are similar. And the scale factor from ππππΏ, which is the larger polygon, to π΄π΅πΆπ·, the smaller polygon, is 0.8.