IXL - Identify similar triangles using the AA and SAS Similarity Theorems (Geometry practice)

Are these scalene triangles similar?

yes

ref_doc_title.

Learn with an example

question

Are these triangles similar?

40°

51°

40°

47°

yes

key idea

Two triangles are similar if and only if they are scaled versions of each other. The ratios of their corresponding side lengths are equal and the measures of their corresponding angles are equal.

solution

Look at the diagram.

40°

51°

40°

47°

Since

∠

51°

∠

40°

and

∠

47°

∠

is not congruent to

∠

Next, check that

∠

is not congruent to

∠

Use the fact that the interior angle sum of a triangle is 180° to solve for

∠

180°

∠

40°

47°

Plug in

∠

40°

and

∠

47°

180°

Plug in

∠

40°

and

∠

47°

∠

87°

Combine like terms

180°

Combine like terms

∠

Subtract 87° from both sides

93°

Subtract 87° from both sides

So,

∠

is not congruent to

∠

either. Therefore, no angle in

△

is congruent to

∠

and the triangles are not similar.

Looking for more? Try these:

Lesson: Similar triangles

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M.3Identify similar figures

Lesson: Similar triangles

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