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Brianne Pizzigoni Similar Triangles Mathematics Grade 3 FORWARD Click on each the following triangles to learn about similar triangles! 1 5 2 5 6 3 4 7 AFTER CLICKING ON EACH TRIANGLES CLICK ON THE STAR FOR YOUR FOLLOW UP MULTIPLE CHOICE QUESTION 8 Ratio CLICK HERE AFTER READING • The first thing you need to know about similar triangles is that Similar Triangles ARE NOT congruent. The sides of the triangle are in ratio/proportion. That means that one triangle is either sized up or down to form another similar triangle. • In triangle Number 5 you will see an example problem on how to solve a ratio question concerning similar triangles. SSS • The SSS property states that when three sides of one triangle are in proportion to three sides of another triangle, than those two triangles are similar. • In Triangle number 6 you will see an example of the SSS Property. CLICK HERE AFTER READING SAS • The SAS property states that when two sides of one triangle are in proportion to two sides of another triangle AS WELL AS the angle in between those two sides are congruent to each other, than the two triangles are similar. • In Triangle number 7 you will see an example of the SAS Property. CLICK HERE AFTER READING AAA • The AAA property states that when three angles of one triangle are congruent to three angles in another triangle, than those two triangles are similar. • In Triangle number 8 you will see an example of the AAA Property. CLICK HERE AFTER READING Example of Ratio The picture above shows an example of how to use the ratio rule to determine similar triangles. In this example the two triangles are similar. This means that side BA corresponds to side YX, side BC corresponds to side YZ, and side AC corresponds to side XZ. This also means that the ratio of these are equal. The ratio of BA/YX equals the ratio of BC/YZ which equals the ratio of AC/XZ. The ratio is ½. You can use this concept to solve missing sides of triangles and to determine if two triangles are similar using the SSS property. CLICK HERE AFTER READING Example of SSS CLICK HERE AFTER READING Using your knowledge of the Ratio Rule you would be able to determine if these two triangles are similar. Side MK is to side PR, side ML is to side PQ, and Side KL is to side QR. That means that in order for these two triangles to be similar the following must be true. MK/PR = KL/QR = ML/PQ OR 10/12 = 20/24 = 15/18 THE TRIANGLES ARE SIMILAR. RATIO = 5/6 Example of SAS You can determine that these two triangles are similar using the SAS Property. You can see that the two given angles are congruent. Also the two sides 4 and 10 of the first triangle are in proportion of the second triangle with sides 2 and 5. That means that 4/2 = 10/5. The two triangles have a ration of ½ or 2 CLICK HERE AFTER READING Example of AAA CLICK HERE AFTER READING You can determine that these two triangles are similar by simply looking at the triangles. You can see that the three angles in the one triangle are congruent to the angles in the other triangle. Keep in mind, if you were only given the two angles of each triangle you would still be able to determine that these two triangles are similar because the angles within a triangle have to equal 180 degrees. MULTIPLE CHOICE QUESTION Only using the given information, which property proves that these two triangles are similar? A- AAA B- SAS C- SSS AAA • INCORRECT; Only one angle of the triangles are given so you can not determine whether the two triangles are similar by this property. CLICK HERE TO TRY AGAIN SAS • CORRECT!!! The two sides of the one triangle are in proportion AS WELL AS the angle in between those two sides are congruent. CLICK HERE SSS • INCORRECT; only two sides of the triangle are given. CLICK HERE TO TRY AGAIN CONGRADULATIONS • YOU HAVE NOW COMPLETED THE LESSON. PLEASE CLICK ON THE ICON BELOW FOR THE NEXT STUDENT.