![]() ![]() The ratio between BC and YZ is also this constant. Is congruent to XYZ, and let's say we know that Know that angle ABC is congruent to angle XYZ. Or if you multiplyīoth sides by AB, you would get XY is some Know that XY over AB is equal to some constant. Less than 1 in which case it would be a smaller value. Actually, let me make XYīigger, so actually, it doesn't have to be. When we go to another triangle, we know that XY is AB And let's say that we know that this side, ![]() Or another way to think about it, the ratioīetween corresponding sides are the same. Really just scaling them up by the same amount, So in general, to go fromĬorresponding side there, we always multiply And what is 60 dividedīy 6 or AC over XZ? Well, that's going to be 10. What is BC over XY? 30 divided by 3 is 10. One over here is 6, 3, and 3 square roots of 3. Numbers because we will soon learn what typical ratiosĪre of the sides of 30-60-90 triangles. Is 30 square roots of 3, and I just made those Right over here is 30, and this right over here Talking about congruence, means that the correspondingīetween corresponding sides are going to be the same. Going to build off of them to solve problemsĪnd prove other things. Similarity postulates or axioms or things that To get these confused with side-side-side congruence. We know we are dealing with similar triangles. Three corresponding sides are the same, then So if you have all threeĬorresponding sides, the ratio between all The ratio between this side and this side- notice we're not The ratio between AB and XY, we know that AB over XY- so So for example, if we haveĪnother triangle right over here- let me Now, the other thing weīetween all of the sides are going to be the same. And you can really justĬonstraints for similarity. Triangle right over here is similar to that one there. We know that on this triangle, this is 90 degrees Put some numbers here, if this was 30 degrees, and If you could show that twoĬorresponding angles are congruent, then we're dealing To show similarity, you don't have to show threeĬorresponding angles are congruent, you really Whatever these two anglesĪre, subtract them from 180, and that's going If you know that this is 30Īnd you know that that is 90, then you know that thisĪngle has to be 60 degrees. You know two of the angles, then you know what the These two triangles are similar? Well, sure. Is congruent to this angle, and that angle right there Two of the corresponding angles are congruent. Let me draw it like this- and if I told you that only Have another triangle that looks like this. Two angles for a triangle, you know the third. But do you need three angles? If we only knew two of theĪngles, would that be enough? Well, sure because if you know B and Y, which are the 90ĭegrees, are the second two, and then Z is the last one. Order right to make sure that you have the rightįirst two things. Know that triangle ABC is similar to triangle XYZ. So we would know from thisīecause corresponding angles are congruent, we would This is 90 degrees,Īnd this is 60 degrees, we know that XYZ in this case, And we have anotherĬlearly a smaller triangle, but it's corresponding angles. ![]() ![]() This angle right over here is 60 degrees. This is 30 degrees, this angle is 90 degrees, and So we already knowĪngles are congruent to the correspondingĪngles on ABC, then we know that we're dealing Whether another triangle is similar to triangle ABC. I want to come up withĪ couple of postulates that we can use to determine Some of these involve ratios and the sine of the given angle. There are some other ways to use SSA plus other information to establish congruency, but these are not used too often. If the given angle is right, then you should call this "HL" or "Hypotenuse-Leg", which does establish congruency. However, you shouldn't just say "SSA" as part of a proof, you should say something like "SSA, when the given sides are congruent, establishes congruency" or "SSA when the given angle is not acute establishes congruency". If the side opposite the given angle is longer than the side adjacent to the given angle, then SSA plus that information establishes congruency. SSA establishes congruency if the given sides are congruent (that is, the same length). SSA establishes congruency if the given angle is 90° or obtuse. However, in conjunction with other information, you can sometimes use SSA. SSA alone cannot establish either congruency or similarity because, in some cases, there can be two triangles that have the same SSA conditions. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |