[tex]\rm \dfrac{HL}{JL}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]
Step-by-step explanation:
Given :
[tex]\rm \bigtriangleup HLI \sim \bigtriangleup JLK[/tex] by the SSS similarity theorem.
[tex]\rm \dfrac {HL}{JL} = \dfrac{IL}{KL}[/tex]
Solution :
According to SSS postulate,
KL = IL ----- (1)
HL = JL ----- (2)
HI = JK ------ (3)
From equation (1), (2) and (3) we get,
[tex]\rm \dfrac{HL}{JL}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]
For more information, refer the link given below
https://brainly.com/question/10376207?referrer=searchResults
Triangle HLI has sides identical in measure to the three sides of triangle JLK, then the two triangles are congruent by SSS postulate. Therefore,
[tex]\rm \dfrac{HL}{JK}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]
Given :
[tex]\rm \Delta HLI \sim \Delta JLK[/tex] by the SSS similarity.
According to SSS (Side Side Side) postulate:
If all three sides of a triangle are congruent to corresponding three sides of other triangle then the two triangles are congruent.
If triangle HLI has sides identical in measure to the three sides of triangle JLK, then the two triangles are congruent by SSS postulate.
Therefore, from triangle HLI and triangle JLK we get,
KL = IL ----- (1)
HL = JL ----- (2)
HI = JK ------ (3)
From equation (1) , (2) and (3) we get,
[tex]\rm \dfrac{HL}{JK}=\dfrac{IL}{KL}=\dfrac{HI}{JK}[/tex]
For more information, refer the link given below
https://brainly.com/question/1593616
