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 they’re congruent or not.

So, if we start with our sides, with side 𝐢𝐷 on our left quadrilateral, we can see from the one marking that this is congruent with side length 𝑂𝑃 on our quadrilateral 𝑂𝑃𝑀𝑁. We can also see that the side 𝐹𝐸 on the quadrilateral 𝐢𝐷𝐸𝐹 is congruent with side 𝑀𝑁 on the quadrilateral 𝑃𝑀𝑁𝑂. We can see that side 𝐢𝐹 is congruent with side 𝑃𝑀 and side 𝐷𝐸 is congruent to side 𝑂𝑁. So, we’ve demonstrated that we have four corresponding sets of congruent sides. However, this isn’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 aren’t the same shape. So, we need to check the angles in our polygons.

So, looking at angle 𝐢 in quadrilateral 𝐢𝐷𝐸𝐹, we could say that this is congruent with angle 𝑀 in quadrilateral 𝑃𝑀𝑁𝑂. Equally, angle 𝐷, which is labelled as 104 degrees, would be congruent with angle 𝑁, which is also 104 degrees. We can see that angle 𝐸 of 76 degrees is congruent with angle 𝑂 of 76 degrees. And our final angle 𝐹 would be congruent with angle 𝑃. So now, we’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.

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