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HELP ME PLEASE!!!

Which triangle is triangle ABC similar to and why?

Options:
1. Triangle ABC is similar to triangle GHI by AA Similarity Postulate.

2. Triangle ABC is not similar to any of the triangles given.

3. Triangle ABC is similar to triangle DEF by AA Similarity Postulate.

4. Triangle ABC is similar to triangle JKLI by AA Similarity Postulate.

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HELP ME PLEASEWhich triangle is triangle ABC similar to and whyOptions1 Triangle ABC is similar to triangle GHI by AA Similarity Postulate2 Triangle ABC is not class=

Respuesta :

It’s GHI because the angle of a triangle equals 180 and 70+70= 140 and 180-140= 40.
msm555

Answer:

1. Triangle ABC is similar to triangle GHI by AA Similarity Postulate.

Step-by-step explanation:

Two triangles are considered similar if they have the same shape but not necessarily the same size.

There are two key properties that define similar triangles:

  • Corresponding angles are equal: The angles in the same position relative to the corresponding sides are equal.
  • Corresponding sides are proportional: The ratios of the lengths of corresponding sides are always the same. This common ratio is called the scale factor.

In this case: Angles are given.

So,

we have In ∆ABC

[tex]m\angle A = 70^\circ [/tex]

[tex]m\angle C = 70^\circ [/tex]

[tex]m\angle B = 180^\circ - 70^\circ - 70^\circ = 40^\circ [/tex] Using sum of interior angles of triangles are supplementary.

So, the similar triangle must contain the angle of 70°, 40° and 70°.

Let's have a look at the picture,

In ∆HGI, we have

[tex]m\angle H = 70^\circ [/tex]

[tex]m\angle G = 40^\circ [/tex]

[tex]m\angle I = 180^\circ - 70^\circ - 40^\circ = 70^\circ [/tex] Using sum of interior angles of triangles are supplementary.

So, the similar triangle to ABC is ∆GHI.

Therefore, the answer is:

1. Triangle ABC is similar to triangle GHI by AA Similarity Postulate.

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