Answer:
a)similar; b)similar; c)similar; d)NOT similar
Step-by-step explanation:
>In general if
all corresponding angels are ≅, and
all corresponding sides are in proportion
then the Δs are similar
>we have 3 similarity theorems AA, SSS, and SAS
a)
we can use that sum of angles in a triangle is 180 to find the missing angles
180-96-32 = 52
so in the smaller triangle the angles are 96°-52°-32°
in the larger triangle the angles given are 52°-32°
Since there are 2 corresponding angles congruent, AA theorem of similarity says that the 2 triangles are similar. The transformations were that the big triangle was shrunk and rotated
b)
here we are given a pair of congruent angles and we need to check if the sides are in proportion, is 14/44.8 equal to 20/64?
14/44.8 =.3125 is equal to 20/64=.3125
since we have two corresponding sides in proportion and the angles in between them congruent the SAS theorem says that the 2 triangles are similar. The transformation was that the small triangle was dilated.
c)
because we are given the 2 angles are congruent we can conclude that the lines NH and SL are parallel. NH║SL let us conclude that ∡H and ∡ L are congruent because 2 parallel lines cut by a transversal (ML in our case) form congruent angles. So ΔMNH is similar to ΔMSL because of AA theorem of similarity (one pair of A was given congruent, one other pair of A we concluded was congruent)
d)
here we have to check if all the sides are in proportion to see if SSS theorem of similarity applies here
18/90 = .2
44/202.4≈.22
58.5/211.2≈.28
.2≠ .22 ≠ .28
since the sides are not in proportion the 2 triangles are NOT similar.
