TenMarks teaches you how to decide whether the figures are similar.
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How to Determine Whether the Figures are Similar Let’s learn about similarity and see if the figures given are similar. How do we do that? We’re given two parallelograms. We are given two parallelograms. If these two are similar, what does that mean? Well, two figures are considered similar when the ratios of their corresponding sides are equal or proportional and the corresponding angles are equal. Two things have to happen. So, let’s see these figures. What are we given? Let’s measure the angles first. So, angle D in the first one equals 126°. Angle A=54°, angle B=126° and angle C=54°. Now, let’s look at the corresponding angles on the second figure. So next, corresponding to D is H. What is the value of H? It’s 126°. Now E which corresponds to A, E corresponds to A is 54°. Corresponding to B is angle F which is 126°. And corresponding to angle C is angle G which is 54°. Are all the angles equal? That is true. So, this condition has been satisfied. Now, let’s look at the ratio of the corresponding sides. So, let’s write down the ratio of the sides. What are the sides? Let’s start here, AD=15ft. I'm not going to write the units because all the units are in feet anyway. So, AD=15, AB=20, BC=10 and CD=10. Now, on the other figure corresponding to AD is EH or EH=6ft, EF which corresponds to AB is 8ft, FG which corresponds to BC, FG corresponds to BC is 4ft and HG or GH=4ft. So if the first statement is true, then the ratio of all of these should be the same. So, what's the ratio of this two? Well, let’s put down 6/15. Is this equal to 8/20? Is this equal to 4/10? It should be equal to 4/10. We can see this two are equal anyway. Now the question is, are these equal? So these two figures are equal, then 6/15 should be equal to 8/20, should be equal to 4/10, should be equal to 4/10. So if that’s the case, let’s actually look at these ratios. Let’s divide 6 and 15, 6/15 in simplest form. Let’s divide both sides by three to give us 6/3 is two, 15/3 is five. So, the first ratio is 2/5. Now, let’s look at the second ratio. Second ratio is 8/20. If I divide both the numerator and denominator by four, we’re getting it divided by four is two, 20/4 is five. Let’s look at 4/10, divide both the numerator and denominator by two, we get 2/5. So as we can see, all of these values equal 2/5 which means that the ratio of the corresponding sides is also equal. So the net result, are this familiar similar? Yes, these figures are similar.