## Are the triangles similar? If they are, write similarity statement and give the scale factor.

Question

Are the triangles similar? If they are, write similarity statement and give the scale factor.

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2022-04-07T08:57:21+00:00 0 Answers 0

## Answers ( 2 )

1. the first one is correct

2. Answer: [tex]triangle RSTsim triangle UVW[/tex]; [tex]frac{5}{6}[/tex]

Step-by-step explanation:

If In two triangles,

Two pairs of sides of two triangles are in same ratio and there are congruent angle between them,

Then By SAS similarity postulate the triangles are similar.

Here In triangles RST and UVW, (According to the given figure)

[tex]frac{RS}{UV} = frac{10}{12} = frac{5}{6}[/tex]

And, [tex]frac{TR}{WU} = frac{15}{18} = frac{5}{6}[/tex]

Thus, [tex]frac{RS}{UV}=frac{TR}{WU}[/tex]

Also, [tex]angle Ucong angle R = 32^{circ}[/tex]

Thus, by SAS similarity postulate,

[tex]triangle RSTsim triangle UVW[/tex]

Also, the scale factor or common ratio is [tex]frac{5}{6}[/tex]

Thus, First Option is correct.