# Video: Checking the Congruence between Two Given Polygons

Are the polygons shown congruent?

02:00

### Video Transcript

Are the polygons shown congruent?

We can remind ourselves that the word congruent means the same shape and size. A better mathematical description is that polygons are congruent if all corresponding sides and interior angles are congruent. If we want to check if these two quadrilaterals are congruent, we need to check all the corresponding sides and angles to see if theyβre congruent or not.

So, if we start with our sides, with side πΆπ· on our left quadrilateral, we can see from the one marking that this is congruent with side length ππ on our quadrilateral ππππ. We can also see that the side πΉπΈ on the quadrilateral πΆπ·πΈπΉ is congruent with side ππ on the quadrilateral ππππ. We can see that side πΆπΉ is congruent with side ππ and side π·πΈ is congruent to side ππ. So, weβve demonstrated that we have four corresponding sets of congruent sides. However, this isnβt sufficient to show that two polygons are congruent. After all, we could, for example, have a rectangle and a parallelogram which have congruent sides. But these clearly arenβt the same shape. So, we need to check the angles in our polygons.

So, looking at angle πΆ in quadrilateral πΆπ·πΈπΉ, we could say that this is congruent with angle π in quadrilateral ππππ. Equally, angle π·, which is labelled as 104 degrees, would be congruent with angle π, which is also 104 degrees. We can see that angle πΈ of 76 degrees is congruent with angle π of 76 degrees. And our final angle πΉ would be congruent with angle π. So now, weβve shown that we also have four corresponding sets of congruent angles. This fits with our definition of congruent polygons. So, yes, these polygons are congruent.