Answer:
The true properties of segment MN are;
1) MN is parallel to CB
2) MN = 2
Step-by-step explanation:
From the figure, we have;
The length of segment AN = 1
The length of segment NC = 2 = 2 × The length of segment AN
The length of segment AM = 1.8
The length of segment MB = 3.6 = 2 × The length of segment AM
The length of segment AC = 1 + 2 = 3
The length of segment AB = 1.8 + 3.6 = 5.4
Therefore, the length of transversal segments AC and AB are proportionally cut by the two lines, MN and CB
By the triangle proportionality theorem, two transversals are proportionally divided when they are crossed by two or more parallel lines
1) Therefore, lines MN and CB are parallel lines
Whereby we have that MN CB, we get;
ΔAMN ~ ΔABC
Therefore;
AN/AC = MN/CB
Plugging in the values, we get;
1/3 = MN/6
NM = 6 × 1/3 = 2
2) MN = 2
The length of segment CB = 6
Therefore, what must about segment MN are;
MN is parallel to CB and MN = 2.
By applying properties of similar triangles we got that MN is equal to 2 units.
Triangles whose shape are same are known as similar triangle .
In the given figure we can see that
in triangle ABC and AMN
AN=1
NC=2
So AC= AN+NC=1+2=3
AM=1.8
MB=3.6
So AB=AM+MB=5.4
[tex]\frac{AN}{NC}=\frac{1}{3} \\\\[/tex]
and
[tex]\frac{AM}{AB} =\frac{1.8}{5.4}=\frac{1}{3}[/tex]
And angle A is common in both triangles
Hence by SAS property triangle ABC and AMN are similar .
So
[tex]\frac{MN}{CB}=\frac{1}{3} \\\\\\\\\frac{MN}{6}=\frac{1}{3} \\\\\\\\MN=2[/tex]
By applying properties of similar triangles we got that MN is equal to 2 units.
To learn more about similar triangles visit:https://brainly.com/question/2644832
