deductive geometry 2

**thereddevils** · October 15th 2009, 07:19 AM

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

THanks .

**Grandad** · October 15th 2009, 07:57 AM

Hello thereddevils

Originally Posted by thereddevils

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

THanks .

I've added some colour to your diagram, marking the given equal angles in red.

Look at the angles in the triangles LPN and LMN. They have the blue one in common. Can you see an angle equal to the yellow one?

Grandad

**thereddevils** · October 15th 2009, 08:14 AM

Originally Posted by Grandad

Hello thereddevilsI've added some colour to your diagram, marking the given equal angles in red.

Look at the angles in the triangles LPN and LMN. They have the blue one in common. Can you see an angle equal to the yellow one?

Grandad

Thanks ! So is it angle PMN ?

**Grandad** · October 15th 2009, 09:04 AM

Originally Posted by thereddevils

Thanks ! So is it angle PMN ?

Correct!

**Grandad** · October 16th 2009, 01:31 AM

Hello thereddevils

Originally Posted by thereddevils

THanks . This is the continuation of the question .
Given that LP=6 cm , PN=4 cm , and NM=5 cm , use similar triangles to calculate the length of LN .

I tried to find 2 triangles which are congruent . Triangle LPN and triangle LNM .

angle LPN = angle LNM
angle PLN=angle MLN
LN = LN

but one is SAA and the other one is ASA .They cant be congruent .

Lost again.

This 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 $LNP$ and $LMN$ 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:

$\frac{LN}{LM}=\frac{LP}{LN}=\frac{NP}{NM}$

Plug in the numbers you've been given, and solve for the side you want.

Grandad

**thereddevils** · October 16th 2009, 03:43 AM

Originally Posted by Grandad

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 $LNP$ and $LMN$ 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:

$\frac{LN}{LM}=\frac{LP}{LN}=\frac{NP}{NM}$

Plug in the numbers you've been given, and solve for the side you want.

Grandad

THanks . I just realised that congruent and similar triangles are different . THanks again Grandad .

**Soroban** · October 16th 2009, 08:23 AM

Hello, thereddevils!

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

Code:

                  N
                  *
                **   *
              * *       *
            *  *           *
          *   *               * .
        *    *                   *
    L *  *  *  *  *  *  *  *  *  *  * M
            P

Make two diagrams . . .

Code:

                  N
                  *
                **
              * *
            *  *
          *   *
        *    *
      *     *
    * 2  1 *
  * * * * * P

Let $\angle 1 = \angle LPN,\;\;\angle 2 = \angle L$

$\angle LNP$ is the third angle of the triangle.

Code:

                  N
                  *
                * 1  *
              *         *
            *              *
          *                   *
        * 2                      *
    L *  *  *  *  *  *  *  *  *  *  * M
            P

We have: . $\angle 1 = \angle LNM,\; \angle 2 = \angle L$

$\angle M$ is the third angle of the triangle.

Therefore: . $\angle LNP \:=\:\angle M$

Edit: Too slow again . . . Too fast for me, Grandad!
.

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