LPM is a straight line and $\displaystyle \angle LPN = \angle LNM $. Name the angle equal to $\displaystyle \angle LNP $ .
THanks .
Hello thereddevilsThis is copied from here, because I think you got the questions mixed up.
Assuming that the quote here refers to the question in this post, note that you need to use similar triangles, not congruent ones. The two triangles $\displaystyle LNP$ and $\displaystyle LMN$ are similar, because their angles are all equal. And the key fact is that corresponding sides - those opposite to equal angles - are in the same ratio. Since we've marked the angles in red, blue and yellow, it's very easy to see which are pairs of corresponding sides. We write their ratio as a set of fractions, like this:
$\displaystyle \frac{LN}{LM}=\frac{LP}{LN}=\frac{NP}{NM}$
Plug in the numbers you've been given, and solve for the side you want.
Grandad
Hello, thereddevils!
LPM is a straight line and $\displaystyle \angle LPN = \angle LNM $.
Name the angle equal to $\displaystyle \angle LNP $Code:N * ** * * * * * * * * * * . * * * L * * * * * * * * * * * M P
Make two diagrams . . .
Let $\displaystyle \angle 1 = \angle LPN,\;\;\angle 2 = \angle L$Code:N * ** * * * * * * * * * * * 2 1 * * * * * * P
$\displaystyle \angle LNP$ is the third angle of the triangle.
Code:N * * 1 * * * * * * * * 2 * L * * * * * * * * * * * M P
We have: .$\displaystyle \angle 1 = \angle LNM,\; \angle 2 = \angle L$
$\displaystyle \angle M$ is the third angle of the triangle.
Therefore: .$\displaystyle \angle LNP \:=\:\angle M$
Edit: Too slow again . . . Too fast for me, Grandad!
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