LPM is a straight line and $\displaystyle \angle LPN = \angle LNM $. Name the angle equal to $\displaystyle \angle LNP $ .

THanks .

Printable View

- Oct 15th 2009, 07:19 AMthereddevilsdeductive geometry 2
LPM is a straight line and $\displaystyle \angle LPN = \angle LNM $. Name the angle equal to $\displaystyle \angle LNP $ .

THanks . - Oct 15th 2009, 07:57 AMGrandad
- Oct 15th 2009, 08:14 AMthereddevils
- Oct 15th 2009, 09:04 AMGrandad
- Oct 16th 2009, 01:31 AMGrandad
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 - Oct 16th 2009, 03:43 AMthereddevils
- Oct 16th 2009, 08:23 AMSoroban
Hello, thereddevils!

Quote:

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 . . .

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!

.