The value of x from the similar angle triangles is given by x = 9
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔADC
where AD is the common side of the two triangles
And , the measure of ∠ADB = measure of ∠ADC
So , the two triangles are similar
And , the measure of AD = 6
The measure of DC = 4
The measure of BD = x
From the similar triangle theorem ,
BD / AD = AD / DC
On simplifying , we get
x / 6 = 6 / 4
Multiply by 6 on both sides , we get
x = 36/4
x = 9
Therefore , the value of x is 9
Hence , the similar triangles is solved and x = 9
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ΔADC and ΔCDB are similar. Therefore the sides are in proportion:
[tex]\dfrac{AD}{DC}=\dfrac{DC}{DB}[/tex]
Substitute:
[tex]\dfrac{x}{6}=\dfrac{6}{4}[/tex] cross multiply
[tex]4x=(6)(6)[/tex]
[tex]4x=36[/tex] divide both sides by 4
[tex]\boxed{x=9}[/tex]
