I just redrew them so I can refer them when we write down here. If we're saying that these two things right over here are similar, that means that corresponding sides are scaled-up versions of each other. So we could say that the length of AB is equal to some scaling factor-- and this thing could be less than some scaling factor times the length of XY, the corresponding sides. So some scaling factor times XY.
We know that the length of BC needs to be that same scaling factor times the length of YZ. And then we know the length of AC is going to be equal to that same scaling factor times XZ. So that's XZ, and this could be a scaling factor. If they're the exact same size, if they're essentially congruent triangles, then these k's will be 1. But another way to write these same statements-- notice, all I'm saying is corresponding sides are scaled-up versions of each other.
And then the second statement right over here, if you divide both sides by YZ-- let me do it in that same color-- you get BC divided by YZ is equal to that scaling factor. And remember, in the example we just showed, that scaling factor was 3. But now we're saying in the more general terms, similarity, as long as you have the same scaling factor.
Or another way to think about it is the ratio between corresponding sides. Notice, this is the ratio between AB and XY. So if you have similar triangles-- let me draw an arrow right over here. Similar triangles means that they're scaled-up versions, and you can also flip and rotate and do all the stuff with congruency.
And you can scale them up or down. Which means all of the corresponding angles are congruent, which also means that the ratio between corresponding sides is going to be the same constant for all the corresponding sides.
Or the ratio between corresponding sides is constant. The length of side AB is 2 cm. Side AB is , and side DE is 6. Two triangles are similar. The corresponding sides have a ratio of If the smaller triangle has a side length of 18 centimeters, what is the measurement of the corresponding side of the larger triangle?
Let ABC be any triangle. To qualify in the exam, 60 percent marks is mandatory. What are the maximum marks for the exam? The ratio of P, Q and R is 3 : 5 : 8 respectively. If their sum is , then what is the difference between P and R?
P and Q alone can do a piece of work in 18 and 45 days respectively. They started the work together and P left after 3 days of starting the work.
Q finished the remaining work alone. In how many days was the work completed? Train 2 leaves B at 10 am and leaves A at 6 pm. Around what time do both trains meet? According to Ptolemy's theorem. Which of the following represents an acute angle?
What is the number of sides of the regular polygon. In the given parallelogram ABCD, what is the value of y? Which of the following is incorrect about the rectangular pyramid? Which of the following represents an obtuse angle? More Quantitative Aptitude Questions Q1. The average speed of Columbus. Which of the following fractions is the largest?
0コメント