Geometry similar triangles

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rachelmaddie

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Is my work correct?
To find the value of x

NM/KM = LN/JK

x/(3+x)= 5/10...................................................edited

Cross multiply

10x = 5(3+x)

10x = 5(3) + 5(x)

10x = 15 + 5x

10x - 5x = 5x

15 = 5x

x = 3

Substitute the value of x to find the measures

KM = 3 +(3) = 6

NM = x = 3FE6FE20B-1817-46E6-8820-FCDEAE9D2B6F.png
 
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rachelmaddie said:
Is my work correct?
To find the value of x

NM/KM = LN/JK

x/3+x= 5/10

Cross multiply

10x = 5(3+x)

10x = 5(3) + 5(x)

10x = 15 + 5x

10x - 5x = 5x

15 = 5x

x = 3

Substitute the value of x to find the measures

KM = 3 +(3) = 6

NM = x = 3View attachment 14344
Click to expand...
Yes except you missed grouping symbols in the first line (without those your "work" would be incorrect.
 
lev888 said:
Missing parentheses again. And you need to justify.
Click to expand...
Hopefully I’ve done a better job of justifying.
The similar triangles are KMJ and NML.
When triangles are similar, the three angle pairs are all equal, therefore the three pairs of sides must also be in proportion.
NM/KM = ML/MJ = NL/KJ
To find the value of x substitute the values into the proportion
NM/KM = LN/JK
NM = x, KM = 3 + x
LN = 5, JK = 10
x/(3+x)= 5/10
Cross multiply to solve for x
10x = 5(3+x)
10x = 5(3) + 5(x)
10x = 15 + 5x
10x - 5x = 5x
15 = 5x
x = 3
Substitute the value of x to find the measures of indicated sides
KM = 3 +(3) = 6
NM = x = 3
 
Very good.
I'd also add in a justification for your reasoning that the two triangles are similar, ie three angle pairs (two given and one consequential) are equal implies similarity.
Your sentence "When triangles are similar, the three angle pairs are all equal" is not the same as "when the three pairs of angles are all equal, the triangles are similar". Can you see the subtle difference there? It's sort of like the chicken and the egg. Firstly, you know (given) that the three pairs of angles are equal, thus implying similarity. Once you have given a reason for similarity (AAA) you can then say the bit about proportionality of sides.
 
Harry_the_cat said:
Very good.
I'd also add in a justification for your reasoning that the two triangles are similar, ie three angle pairs (two given and one consequential) are equal implies similarity.
Your sentence "When triangles are similar, the three angle pairs are all equal" is not the same as "when the three pairs of angles are all equal, the triangles are similar". Can you see the subtle difference there? It's sort of like the chicken and the egg. Firstly, you know (given) that the three pairs of angles are equal, thus implying similarity. Once you have given a reason for similarity (AAA) you can then say the bit about proportionality of sides.
Click to expand...
When the three pairs of angles are all equal, the triangles are similar (two given and one consequential implies similarity.)
Therefore the three pairs of sides must also be in proportion
 
Harry_the_cat said:
Your answer in post #8 is correct.
Click to expand...
The similar triangles are KMJ and NML.
When the three pairs of angles are all equal, the triangles are similar (two given and one consequential implies similarity.)
Therefore the three pairs of sides must also be in proportion.
NM/KM = ML/MJ = NL/KJ
To find the value of x substitute the values into the proportion
NM/KM = LN/JK
NM = x, KM = 3 + x
LN = 5, JK = 10
x/(3+x)= 5/10
Cross multiply to solve for x
10x = 5(3+x)
10x = 5(3) + 5(x)
10x = 15 + 5x
10x - 5x = 5x
15 = 5x
x = 3
Substitute the value of x to find the measures of indicated sides
KM = 3 +(3) = 6
NM = x = 3
 
rachelmaddie said:
Is my work correct?
To find the value of x

NM/KM = LN/JK

x/(3+x)= 5/10...................................................edited
Click to expand...
First, no matter which method used, you should reduce 5/10 to 1/2.
Now I notice that in \(\displaystyle \frac{x}{x+3}\) that the denominator is 3 more than the numerator. So I write \(\displaystyle \frac{1}{2}\) in a similar way as \(\displaystyle \frac{3}{6}\).

Now I have \(\displaystyle \frac{x}{x+3}\) = \(\displaystyle \frac{3}{6}\) and now I can equate the numerators or denominators. So I get x=3 (or x+3=6 => x=3).
 
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