IXL - Similarity and altitudes in right triangles (Geometry practice)

and

what is

MN?

Write your answer as a whole number or as a decimal rounded to the nearest hundredth.

MN =

ref_doc_title.

Learn with an example

question

and

what is

LM?

Write your answer as a whole number or as a decimal rounded to the nearest hundredth.

LM =

key idea

The AA Similarity Theorem states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle.

△

∠

≅

∠

and

∠

≅

∠

solution

You can use similar triangles to write a proportion. Then, plug in the lengths you are given and solve for

LM.

First, notice that △KML and △JKL both have right angles. They also have ∠L in common. So, △KML and △JKL are similar by the AA Similarity Theorem.

Since △KML and △JKL are similar, the ratios of corresponding sides are equal.

Plug in

and

and solve for

LM.

196

LM = 11.5294...

To the nearest hundredth,

11.53

Looking for more? Try this:

Lesson: Similar triangles

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Work it out

Not feeling ready yet? These can help:

M.8Similarity rules for triangles

Lesson: Similar triangles

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