What makes 2 polygons similar

For example, all equilateral triangles are similar and all squares are similar. If two polygons are similar, we know the lengths of corresponding sides are proportional. In similar polygons, the ratio of one side of a polygon to the corresponding side of the other is called the scale factor. The ratio of all parts of a polygon including the perimeters, diagonals, medians, midsegments, altitudes is the same as the ratio of the sides.

What if you were told that two pentagons were similar and you were given the lengths of each pentagon's sides. How could you determine the scale factor of pentagon 1 to pentagon 2? All the corresponding angles are congruent because the shapes are rectangles.

Based on the similarity statement, which angles are congruent and which sides are proportional? Just like in a congruence statement, the congruent angles line up within the similarity statement.

Note that the proportion could be written in different ways. For questions , determine whether the following statements are true or false. Determine if the following triangles and quadrilaterals are similar. If they are, write the similarity statement. Similar Polygons Similar polygons are two polygons with the same shape, but not the same size.

Scale Factors Think about similar polygons as enlarging or shrinking the same shape. Are these two rectangles similar? Solution Just like in a congruence statement, the congruent angles line up within the similarity statement. Review For questions , determine whether the following statements are true or false.

Quadrilaterals are polygons that have four sides. The sum of the interior angles of a quadrilateral is degrees. Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same the fourth angles automatically become the same as the interior angle sum is degrees , and two adjacent sides have equal ratios.

Let us discuss the similarity of squares. According to the similarity of quadrilaterals, the corresponding angles of similar quadrilaterals should be equal.

We know that all angles are 90 degrees in the square, so all the corresponding angles of any two squares will be the same. All sides of a square are equal. In a Rhombus, all the sides are equal. So, just like squares, rhombuses satisfy the condition of the ratio of corresponding sides being equal.

In a Rhombus, the opposite sides are parallel, and hence the opposite angles are equal. But the value of those angles can be anything. So, it can very much happen that two rhombuses have different angles. Hence, all rhombuses are not similar. Two rectangles are similar when the corresponding adjacent sides have the same ratio. We do not need to check the angles as all angles in a rectangle are 90 degrees.

No, all rectangles are not similar rectangles. The ratio of the corresponding adjacent sides may be different. Here the ratios will not be equal. Two rectangles are called congruent rectangles if the corresponding adjacent sides are equal. It means they should have the same size. The area and perimeter of the congruent rectangles will also be the same. Similarity and congruency are some important concepts of geometry.

A solid understanding of these topics helps in building a good foundation in geometry. Well if we look at these two figures and let's say they're similar, we can see that the sides that correspond are definitely not going to be congruent.

So the corresponding angles must be congruent. Secondly, and again it has to be both of these for them to be similar. Corresponding sides must be proportional. So what that means is if I said that these two figures were similar, that is if a, b, c, d, e and I'm going to write that over here. If a, b , c, d, e pentagon and this figure f, g, h, I, j, g, h, i, j are similar, notice it kind of looks like a congruence marking except for we do not have the equal sign.

So if you just have Mr. Squiggles all by himself, then that means that they're similar. So what that means is that the ratio of ab:fg is the same as bc:gh of cd:hi and so on.

So the way that you check if two figures are similar corresponding angles must be exactly the same, they must be congruent, and the corresponding sides must be proportional. All Geometry videos Unit Similarity.