Which is the best strategy to use to solve this problem?
2 answers:
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Given: We have the given figure through which we can see
LK=16,
KJ=10,
LM=24,
MN=15
To Find: Whether KM || JN and the reasoning behind it.
Solution: Yes, KM || JN because
Explanation:
For this solution, we use the concept of Similar Triangles.
Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).
Now, ∠MLK=∠NLJ
To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN
which is true as both sides simplify to
Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).
Therefore, KM || JN.
To come to the reasoning, notice that
In other words,
Answer:
x = 10
Step-by-step explanation:
Since the triangles are similar the ratios of corresponding sides are equal
=
, that is
=
( cross- multiply )
20(4x + 2) = 84x
80x + 40 = 84x ( subtract 80x from both sides )
40 = 4x ( divide both sides by 4 )
x = 10