Answers
Answer:
Given :
ΔBCD ≈ ΔFGE
x = 6
FG = 4x + 2 = 4 × 6 +2 = 26
EF = 5x - 2 = 5 × 6 -2 = 28
Step-by-step explanation:
The value of the side FE of the triangle FGE is FE = 28
What are Congruent Triangles?
Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔBCD
Let the second triangle be ΔEFG
Now , the triangle BCD and triangle EFG are similar by congruency
So , From the congruent triangle theorem ,
ΔBCD ≅ ΔEFG
So , the sides are congruent from the theorem
BD / FE = CB / FG
Substituting the values in the equation , we get
42 / ( 5x - 2 ) = 39 / ( 4x + 2 )
Cross multiplying the equations , we get
168x + 84 = 195x - 78
Subtracting 168x on both sides of the equation , we get
27x -78 = 84
Adding 78 on both sides of the equation , we get
27x = 162
Divide by 27 on both sides of the equation , we get
x = 6
So , substitute the value of x from the sides FE and FG , we get
The value of FE = 5x - 2
The value of FE = 5 ( 6 ) - 2
The value of FE = 30 - 2
The value of FE = 28
Therefore , the value of FE is 28
Hence , The value of the side FE of the triangle FGE is FE = 28
To learn more about congruent triangles click :
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