traingle LMN ~ triangle TUV
How long is segment LN and how long is segment UV?
On triangle LMN LM=15 MN=27
On triangle TUV TU=10 TV=20
Sides LM & TU are congruent on each triangle
Sides MN & UV are congruent
Sides LN & TV are congruent
I don't understand how to find the missing sides of LN & UV on each triangle? Do I multiply or divide
To find the lengths of segments LN and UV in the given triangles, we can use the concept of similar triangles. Similar triangles have the same shape but may differ in size.
In this case, we are given that triangle LMN is similar to triangle TUV. This means that the corresponding angles of the triangles are equal and the corresponding sides are proportional.
Since sides LM and TU are congruent, we can write the following ratio:
LM/TU = LN/UV
Substituting the given values:
15/10 = LN/UV
To solve for LN, we can cross-multiply:
15 * UV = 10 * LN
Similarly, since sides MN and UV are congruent, we can write the following ratio:
MN/UV = LN/UV
Substituting the given values:
27/20 = LN/UV
To solve for UV, we can cross-multiply:
27 * UV = 20 * LN
To find the missing sides LN and UV, divide both sides of the equations by the respective coefficients of UV and LN:
For LN: LN = (15 * UV) / 10
For UV: UV = (27 * UV) / 20
When dividing, note that the variables remain on the same side of the equation, and we divide by the coefficient on each side to isolate the variable.
Now you can substitute the values of UV given in triangle TUV to solve for LN, and vice versa to solve for UV.
To find the missing sides LN and UV on each triangle, you can use the property of similar triangles. Since triangles LMN and TUV are similar, their corresponding sides are proportional.
To find the length of segment LN, you can set up the following proportion:
LM/LN = TU/UV
Substituting the given values:
15/LN = 10/UV
Cross-multiplying:
15 * UV = 10 * LN
Dividing both sides by 10:
3 * UV = 2 * LN
To find the length of segment UV, you can set up the following proportion:
MN/UV = LN/TV
Substituting the given values:
27/UV = LN/20
Cross-multiplying:
27 * 20 = UV * LN
Dividing both sides by 27:
20 * LN = UV * 27
I don't see how you can say that LM ≅ TU, and then say that LM=15 and TU=10.
Also, when you say LMN ~ TUV that implies that the vertices are listed in the same respective order. That is,
LM ~ TU
MN ~ UV
NL ~ VT
But that's not the case here.