If triangle LMN ~ triangle PON, what is MN?
2 answers:
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1. , then
and triangles ADC and ACB are similar by AAA theorem.
2. The ratio of the corresponding sides of similar triangles is constant, so
.
3. Knowing lengths you could state that .
4. This ratio is equivalent to .
5. , then
and triangles BDC and BCA are similar by AAA theorem.
6. The ratio of the corresponding sides of similar triangles is constant, so
.
7. Knowing lengths you could state that .
8. This ratio is equivalent to .
9. Now add results of parts 4 and 8:
.
10. c is common factor, then:
.
11. Since you have
.