Can anyone please post proving exercises involving the SAS similarity theorem?

Question

Here is a link to an example of what I need: http://img.photobucket.com/albums/v705/linsauke/Image2.jpg


I desperately need assistance on this right now so anyone with a good heart and a time to spare, PLEASE help... thanks!

Okay, i forgot to say, I know that my example is for AA similarity.. I was just hoping that someone can make a similar exercise but for SAS similarity. And yes, there is an SAS theorem for similarity. Thanks!

Answer 1

While the above answerer is correct that there is an SAS theorem for proving triangles congruent, there is also an SAS theorem for proving triangles similar: If two sides of one triangle are proportional to two corresponding sides of another triangle, and their included angles are congruent, then the triangles are similar. So SAS can in fact be used to prove triangles are similar.

Answer 2

Years in the past, a guy named Pythagoras found a tremendous truth about triangles: If the triangle had a good attitude (ninety°) ... ... and also you made a sq. on all the three aspects, then ... ... the biggest sq. had the very similar section as the different 2 squares practice! The longest area of the triangle is termed the "hypotenuse", so the formal definition is: In a good angled triangle the sq. of the hypotenuse is an similar because the sum of the squares of the different 2 aspects. So, the sq. of a (a²) plus the sq. of b (b²) is an similar because the sq. of c (c²): a2 + b2 = c2 confident ... ? enable's see if it extremely works utilizing an party. A "3,4,5" triangle has a good attitude in it, so the formula could artwork. enable's examine if the parts are an similar: 32 + 40 2 = 52 Calculating this turns into: 9 + 16 = 25 sure, it extremely works ! Why is this valuable? If all of us recognize the lengths of two aspects of a good angled triangle, then Pythagoras' Theorem facilitates us to locate the length of the third area. (yet bear in mind it purely works on good angled triangles!) How Do i exploit it? Write it down as an equation: a2 + b2 = c2 you may now use algebra to locate any lacking value, as interior good the following examples: a2 + b2 = c2 52 + 122 = c2 25 + 100 and forty four = 169 c2 = 169 c = ?169 c = 13 a2 + b2 = c2 ninety 2 + b2 = 152 80 one + b2 = 225 Take 80 one from each and each and every area b2 = 100 and forty four b = ?100 and forty four b = 12 and also you'll instruct It your self ! Get paper pen and scissors, then utilizing good the following animation as a handbook: Draw a good angled triangle on the paper, leaving a good number of area. Draw a sq. alongside the hypotenuse (the longest area) Draw an similar sized sq. on the different area of the hypotenuse Draw lines as shown on the animation, like this: reduce out the shapes manage them that you'll instruct that the large sq. has an similar section as both squares on the different aspects yet another, Amazingly ordinary, information the following is between the oldest proofs that the sq. on the lengthy area has an similar section as the different squares. Watch the animation, and pay interest even as the triangles commence sliding round. you may want to favor to observe the animation some cases to appreciate what's happening. The red triangle is the genuine one. We actually have a proof by including up the parts. historic observe: even as we call it Pythagoras' Theorem, it replaced into also common by Indian, Greek, chinese and Babylonian mathematicians nicely formerly he lived !

Answer 3

I looked at you example problem and will give you rhe proper steps tp prove it. But first you should realize that SAS is a method to prove triangles are congruent, that is all corresponding angles are equal and all corresponding sides are equal.

Similarity requires only that two angles of one triangle are equal to two angles of the another triangle. So SAS has nothing to do with the problem you have given as an example.

Here are the propert statements and reasons:
S1) GE parallel EL R1) Given
S2) angle NOG= angle NLE R2) If 2 parallel lines are cut .....
S3) angle N = angle N R3) Reflexive or identity property
S4) triangle NGO similar Triangle NEL R4) 2 triangles have 2 angles of one = to 2 angles of ither are similar.
S5) NE/EL = NG/GO R5) Corresponding sides of similar triangle ar proportional.
S6) (NE)(GO)= (GE)(EL) R6) The product of the means = the product of the extremes.

Hope this was not too difficult to followr. Just remember that SAS and ASA, and SSS are methods of proving two triangles congruent which means one triangle can fit exactly on the other.

Similarity means that the two triangles have the same shape but, but not the same size.

A ratio is the quotient of two quanties A proportion is an equation of to ratios such as a/b = c/d

In the above proportion a and d are called the extremes and b and c are called the means. The product of the extremes are always equal to the product of the means.

Thus 5/7= 8/x.
Then 5x=8*7
x=56/5

Hope that helps.

Answer 4

1. 2.common 3. 4.By AAA maxim
5.NE/EL=GO/GE
6.GE/NE=GO/EL cross multiplying