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a. similar by AA
b. similar by SAS
c. similar by SSS
d. not similar
Similar triangles have sides in the same ratio. In these two triangles two corresponding sides are equal. 12 and 12.
Now here for similarity all three sides of the two triangles must be equal but here one is 14.4 and 10.
So these are not similar
but it also has 4 similar angles so would it be similar by sas?
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and 2 corresponding sides
If it had all the 6 angles equal then only it can be proven similar
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a. similar by AA
IF the markings on angles O and L are indications that they are congruent.
IF so, they form one pair of congrent angles and a second pair would be the vertical angles at point Z.
By the AA Triangle Similarity Postulate, that's all that is required for similarity.
The triangles are similar with the following correspondence of vertices:
L <--> O, M <--> N, and Z <--> Z.
Segment OZ does not correspond to Segment ZM. Therefore, there is no conflict with 12 to 12 and a one to one ratio.
No segment lengths at all are needed for this problem IF it is true that angles O and L are congruent.
Note: Congruence of triangles is a special case of similarity of triangles in which the ratio of corresponding sides is 1 to 1.