l>Maths Unit 25 - Euclidean Geometry: Similarity - 3. Conditions for comparable polygons

two polygons are comparable iff ...

You are watching: If two polygons are similar, then the corresponding sides must be

We speak two numbers are comparable if they have actually the same shape, but not necessarily the same size.If they also have the same size, us say they space congruent.Which of these statements space true?If two numbers are similar, climate they are additionally congruent.If two figures are congruent, then they are likewise similar.

There space two problems (tests) for 2 polygons to it is in similar:

all the equivalent angles have to be equal, and every the matching sides have to be proportional.
therefore the an interpretation is: 2 polygons are similar iff they are equiangular and also their equivalent sides space proportional. Let"s look in ~ the importance of solve both problems for polygons.

Are equiangular polygons similar? This applet provides a quick and also definite answer.

The environment-friendly quadrilateral has its vertices on currently parallel to the sides of the blue quadrilateral. So the 2 quadrilaterals are equiangular.But carry out they have actually the same shape?Drag the red points and also judge visually ...!
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Do they have the exact same shape? open the comparable Quadrilaterals applet:


In the applet, the political parties of the smaller sized quadrilaterals room parallel to the political parties of the bigger quadrilaterals, so the quadrilaterals are equiangular in both cases. Connect with the applet and also explain why:

The political parties of AB¢C¢D¢ and also ABCD are nearly never proportional, for this reason they are nearly never similar, i.e. They execute not have actually the exact same shape (find at least one instance for which they room similar). The political parties of PQ¢R¢S¢ and also PQRS are always proportional, so they are always similar, i.e. They have the very same shape.

Two counter examples open up the comparable or not? applet:


The applet shows two basic examples to show conclusively the for polygon to be similar, they have to be both equiangular and proportional.

In the applet, drag points P and also B … do you agree that: In the left figure, rectangles ABCD and APQD are always equiangular, however their sides are nearly never proportional, for this reason they space not comparable (find at least two positions because that which the rectangles are similar). In the right figure, the sides of rectangle ABCD and parallelogram APQD are always proportional, however they are nearly never equiangular, so they are not similar (find 2 positions for which they are similar).