Answer:
Step-by-step explanation:
Looking at the two triangles ΔJKL and ΔJMN and given that JL = JN/3 and JK = JM/3 we can prove the two triangles are similar as follows\
~ From JL = JN/3 and JK = JM/3 we see that
JL/JN = 1/3 = JL/JM
~ This means corresponding sides of the two triangles are proportional i.e. JL corresponds to JN and JK corresponds to JM
By the Triangle Proportionality Theorem. if two sides of one triangle are proportional to the other two sides of another triangle, then the third sides are also proportional.
This means that KL/MN = 1/3 also
Therefore all three sides of ΔJKL are proportional to all three corresponding sides of ΔJMN and by the SSS theorem the two triangles are similar
PROVED
SSS Similarity Criterion:
The SSS similarity theorem states that two triangles are similar if the corresponding ratio of all three sides in the two triangles is equal.
