Respuesta :

Answer:

KJ = 6 , LW = 3 , KJ = 6

Step-by-step explanation:

Let LW be x then KJ be x + 3

In ΔKHJ and ΔLGW,

∠K = ∠L and ∠H = ∠G , So, by AA Similarity, [tex]\Delta KHJ \sim\Delta LGW[/tex]

Therefore,

[tex]\frac{8}{4}=\frac{x+3}{x} =\frac{HJ}{2.5}[/tex]

First taking,

[tex]\frac{8}{4}=\frac{x+3}{x}\\8\cdot x = 4\cdot x + 12\\4\cdot x=12\\x=3[/tex]

∴LW = 3 , KJ = 6

Now,

[tex]\frac{8}{4}=\frac{HJ}{2.5}[/tex]

⇒ HJ = 5


Ver imagen PhantomWisdom

The unknown sides of the triangle KHJ and triangle LGW are HJ = 5, LW = 3, and KJ = 6 and this can be determined by using the given data.

Given :

  • m∠K=m∠L
  • m∠H=m∠G
  • KH = 8, LG = 4, GW = 2.5, and KJ = LW + 3

Given that m∠K = m∠L, m∠H = m∠G, therefore, triangle △KHJ and △LGW are congruent to each other by AA similarity postulate.

To determine the unknown sides of the given triangles, first, let the unknown side LW be 'a' and the side KJ be 'a + 3'.

[tex]\rm \dfrac{8}{4}=\dfrac{a+3}{a}=\dfrac{HJ}{2.5}[/tex]  -----  (1)

[tex]2\times a = (a+3)\times 1[/tex]

2a = a + 3

a = 3

Put the value of 'a' in equation (1).

[tex]\rm \dfrac{3+3}{3}=\dfrac{HJ}{2.5}[/tex]

[tex]\rm 2\times 2.5 = HJ[/tex]

HJ = 5

LW = 3

KJ = 3 + 3 = 6

The unknown sides of the triangle KHJ and triangle LGW are HJ = 5, LW = 3, and KJ = 6 and this can be determined by using the given data.

For more information, refer to the link given below:

https://brainly.com/question/23790352

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