7.7. SAS Similarity http://www.ck12.org
(^6) B∼= (^6) Zbecause they are both right angles. Second,^1015 =^2436 because they both reduce to^23. Therefore,X ZAB=BCZY
and 4 ABC∼4X ZY.
Notice with this example that we can find the third sides of each triangle using the Pythagorean Theorem. If we were
to find the third sides,AC=39 andXY=26. The ratio of these sides is^2639 =^23.
Example B
Are there any similar triangles? How do you know?
(^6) Ais shared by 4 EABand 4 DAC, so it is congruent to itself. IfAEAD=ABACthen, by SAS Similarity, the two triangles
would be similar.
9
9 + 3
=
12
12 + 5
9
12
=
3
4
6 =
12
17
Because the proportion is not equal, the two triangles are not similar.
Example C
From Example B, what shouldBCequal for 4 EAB∼4DAC?
The proportion we ended up with was 129 =^346 =^1217 .ACneeds to equal 16, so that^1216 =^34. Therefore,AC=AB+BC
and 16= 12 +BC.BCshould equal 4 in order for 4 EAB∼4DAC.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52549CK-12 Foundation: Chapter7SASSimilarityB
Vocabulary
Two triangles aresimilarif all their corresponding angles arecongruent(exactly the same) and their corresponding
sides areproportional(in the same ratio).