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FrostGD

Givn : OK = 3, OJ = 30, KN = 1, JM = 3

ON=OK+KN=3+1=4

OM=OJ+JM=30+10=40

In triangles OKJ & ONM,

OKOJ=330=110

ONOM=440=110

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means KJNM=110 or the two sides are parallel.

Hence ˆK=ˆN,ˆJ=ˆM corresponding angles.

akposevictor

Two sides in each triangle that are proportional to each other, and a corresponding included angle in both triangles that are congruent, both triangles are similar.

  • The similarity statement is: [tex]\triangle NOM \sim \triangle KOJ[/tex]
  • Theorem: Side-Angle-Side Similarity Theorem (SAS)

Recall:

Two triangles can be proven to be similar by the SAS Similarity Theorem, if they both have two pairs of corresponding side lengths that are proportional to each other and also have a corresponding included angle that is congruent to each other.

Using the image given, let's determine if two of the given side lengths of each triangle are proportional to each other.

Given:

  • OJ = 30
  • OM = 30 + 10 = 40
  • OK = 3
  • ON = 3 + 1 = 4

  • Thus:

[tex]\frac{OM}{OJ} = \frac{ON}{OK}[/tex]

  • Substitute

[tex]\frac{40}{30} = \frac{4}{3}[/tex] (proportional)

Also, <NOM and <KOJ are congruent to each other (included angles).

Therefore, since we have two sides in each triangle that are proportional to each other, and a corresponding included angle in both triangles that are congruent, both triangles are similar.

The similarity statement is: [tex]\triangle NOM \sim \triangle KOJ[/tex]

Theorem: Side-Angle-Side Similarity Theorem (SAS)

Learn more here:

https://brainly.com/question/11361067

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