I need help proving these two triangles are similar! ?

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Answer 1 · 2018-02-11T07:13:32

As proved below

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Given $HI = LH = 3, LJ = JN = 2.5$

This shows, HJ and IN are parallel and IL and JK are parallel.

Consider triangles LJH & LNI.

$LhatJH = LhatNI$ corresponding angles as HJ parallel IN

Similarly, $LhatHJ = LhatIN$ Again corresponding angles as IL & JK are parallel.

$JhatLH = NhatLI$ common angle.

Hence the two triangles LJH & LNI are SIMILAR.

Corresponding sides are in same proportion.

$(LJ) / (LN) = (LH) / (LI) = (JH) / (NI)$