Refer to the picture above. are these two triangles similar? if so, what is the theorem that allows you to state that these triangles are similar?
a)yes they are similar side-angle-side (sas) similarity theorem
b)yes they are similar by side-side-side (sss) similarity theorem
c)these triangles are not similar.

2) what is the length of segment lp?
a) 13.75
b)35.2
c)23.2

Question 1

We first determine all pairs of side that correspond

Side GE correspond with side IJ
Side EF correspond with side KI
Side FG correspond with side JK

Then we see if all pairs have the same ratio of their length

GE : IJ = 90 : 120 = 3 : 4
EF :  IK = 117 : 156 = 3 : 4
FG : JK = 135 : 180 = 3 : 4

Since all sides have the same ratio, hence triangle GEF is similar to the triangle JIK by properties SSS

Question 2

We start by listing all the corresponding sides

Side LO correspond with side LM
Side LP correspond with side LN
Side OP correspond with NM

We can then write down each pair in term of the ratio of their side length
LO : LM =  22 : 30 = 11 : 15
LP : LN =  = 

Although we don't know the measurement of side OP and NM, we have enough information to solve the problem

We know from the ratio that side LM is  times side LO
so side LN is also  times side LP











Length of line segment LP is 1.75+12=13.75 (option A)