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 $H I = L H = 3, L J = J N = 2.5$ $HI = LH = 3, LJ = JN = 2.5$

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

Consider triangles LJH & LNI.

$L ˆ J H = L ˆ N I$ $LhatJH = LhatNI$ corresponding angles as HJ parallel IN

Similarly, $L ˆ H J = L ˆ I N$ $LhatHJ = LhatIN$ Again corresponding angles as IL & JK are parallel.

$J ˆ L H = N ˆ L I$ $JhatLH = NhatLI$ common angle.

Hence the two triangles LJH & LNI are SIMILAR.

Corresponding sides are in same proportion.

$\frac{L J}{L N} = \frac{L H}{L I} = \frac{J H}{N I}$ $(LJ) / (LN) = (LH) / (LI) = (JH) / (NI)$