Download 100130811.2 Similar Triangles

11.2 Similar Triangles
Recall that in order to be able to tell if triangles were congruent, we did not need to prove all sides and angles
were congruent. We knew the triangles were congruent if we could prove SSS, SAS, AAS, or ASA. In these
investigations, we are going to attempt to find out which shortcuts will work for similar triangles. However, for
similar triangles, when we use “S” in a shortcut, we don’t mean that the sides are congruent, but rather that the
sides are proportional.
Investigation 1: Is AA a similarity shortcut?
1.) If you know that 2 angles in one triangle are congruent to 2 angles in another triangle, do you know that
the third angle is also congruent? Clearly explain your answer.
2.) Draw any triangle CAT.
3.) Measure the angles of your triangle with a protractor and then draw either a larger triangle or a smaller
triangle whose angles have the exact same measures. Label this triangle DOG.
4.) Write 3 ratios for each of the corresponding sides of the triangles.
5.) Using your ratios from above, are the corresponding sides proportional? Show or explain how you
know.
6.) Is AA a similarity shortcut?
Investigation 2: Is SSS a similarity shortcut ?
1.) Draw a triangle and label it NIP.
2.) Either double the sides or cut the sides in half and draw another triangle using those side lengths. Label
it TUK(By doubling or cutting in half, you are ensuring that the new triangles sides are proportional.)
3.) Measure the corresponding angles of the two triangles. Are they congruent?
4.) Is SSS a similarity shortcut?
Investigation 3: Is SAS a similarity shortcut?
1.) Draw a triangle and label it BIG.
2.) Pick any two sides and the angle included between them. Either double the lengths of the sides or cut
them in half. Keep the angle the same and draw another triangle with these measurements. Label it
ONE.
3.) Measure sides and angles and tell if SAS is a similarity shortcut. Explain how you know.