Question

TTriangle H L I is shown. Line segment J K is drawn near point L to create triangle J L K. If △HLI ~ △JLK by the SSS similarity theorem, then StartFraction H L Over J L EndFraction = StartFraction I L Over K L EndFraction is also equal to which ratio? StartFraction H I Over J K EndFraction StartFraction H J Over J L EndFraction StartFraction I K Over K L EndFraction StartFraction J K Over H I EndFraction

Answer 1

Question:

$\triangle$HLI is shown. Line segment JK is drawn near point L to create $\triangle$JLK. If $\triangle$HLI ~ $\triangle$JLK by the SSS similarity theorem, then $\frac{HL}{JL} =\frac{IL}{KL}$ is also equal to which ratio?

$\frac{H I}{J K}$      $\frac{H J}{J L}$     $\frac{I K}{K L}$     $\frac{J K}{H I}$      

Answer:

$\frac{H I}{J K}$

Step-by-step explanation:

Given

HLI ~ $\triangle$JLK

$\frac{HL}{JL} =\frac{IL}{KL}$

Required

Which other ratio equals $\frac{HL}{JL} =\frac{IL}{KL}$

$\triangle$HLI ~ $\triangle$JLK  implies that:

HL, IL and HI corresponds to JL, KL and JK respectively.

So, the possible ratios are:

HL : IL : HI = JL : KL : JK

Convert to fractions

$\frac{HL}{JL} = \frac{IL}{KL} = \frac{HI}{JK}$

So, from the list of options

$\frac{H I}{J K}$ is equivalent to $\frac{HL}{JL} =\frac{IL}{KL}$

Answer 2

^

The answer is A

I got it right