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Polygons - Problem 2 2,637 views

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

If two polygons are congruent, the corresponding angles are congruent, and the corresponding angles are congruent.

You can determine which segments of the polygon are congruent by their position in the polygon's name. For example, given two quadrilaterals ABCD ≅ XYWZ, you know that AB ≅ XY, BC ≅ YW, CD ≅ WZ, and AD ≅ XZ.

Likewise, from the order of the letters in these polygons, you know ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠W, and ∠D ≅ ∠Z.

When two polygons are congruent what that means is that corresponding sides are congruent and the corresponding angles are congruent.

So here I’ve drawn two different quadrilaterals and I’ve told you that ABCD is congruent to XYWZ. I’m asking you to list congruent sides and congruent angles. So this will help us develop this idea of corresponding sides and corresponding angles.

If we start off with corresponding sides, let’s look at the first two letters and my first quadrilateral which are AB. Now what corresponds to AB in my other quadrilateral are the first two letters. So I can say that line segment AB I’m going to mark with one congruence marking is congruent to line segment XY.

So I’m going to write that over here that XY is congruent to AB. And I know that because they are corresponding because of the order. So if I look at the next two I see that I have BC and YZ. So if I go over here I can say that line segment BC must be congruent to YW.

So I can go over there and say BC congruent to YW and notice that I’m not saying that these are necessary congruent to everything else just that these two corresponding sides must be congruent.

And doing our third pair of sides we CD and we have WZ, so I see that CD I’m going to mark that with three and WZ 1, 2, 3 so and say CD line segment congruent to WZ line segment and at last we see that our first letter is A our last letter is D so AD I’m going to write with four congruence markings and our first letter is X and our last letter is Z so this had four congruence markings.

So I’m going to mark that AD is congruent to XZ. So that’s just one piece of congruent polygons is that all the corresponding sides are congruent. Also all corresponding angles are congruent and that’s a little bit easier because each of these letters represent a vertex in this polygon.

So the first letter in each of these polygons those angles must be congruent. So I can say that angle A must be congruent to the first letter in this polygon which is angle X. And then my next set is B and Y so I’m going to say that angle B must be congruent to angle Y.

My third set is C and w so I will, say angle C is congruent to angle W. My last letters are D and Z so angle D is congruent to angle Z so we said that corresponding sides and corresponding angles are congruent we are saying based on the order that these letters are in you can determine which sides are corresponding and which angles are corresponding and they always are congruent when you have congruent polygons.

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