Question

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side J L, forming a right angle.

Which similarity statements are true? Check all that apply.


△JKL ~ △KML

△JKM ~ △JKL

△JKM ~ △KML

△JMK ~ △JKL

△JMK ~ △KML

Answer 1

1,4, and 5

Explanation:

Answer 2

1, 4, 5

Explanation:

Consider right triangle JKL with right angle JKL and height KM. This height divides triangle into two right triangles KML and KMJ.

Note that

`m\angle MKL=90^(\circ)-m\angle MLK=m\angle KJM\\ \\m\angle JKM=90^(\circ)-m\angle KJM=m\angle MLK`

So, by AA theorem, we have three similar triangles

`\triangle JKL\sim \triangle JMK\sim \triangle KML`

So, options 1, 4 and 5 are true