ΔABC and ΔDEF are similar to each other by SAS similarity rule .
What are similarity of triangles?
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
There are three major types of similarity rules
- AA (or AAA) or Angle-Angle Similarity Theorem
- SAS or Side-Angle-Side Similarity Theorem
- SSS or Side-Side-Side Similarity Theorem
According to the question
Frances drew ΔABC and ΔDEF
In ΔABC
AB[tex]\frac{AB}{DE} = \frac{AC}{DF}[/tex] = 4
AC = 6
In ΔDEF
DE = 8
DF = 12
Now,
In ΔABC and ΔDEF
[tex]\frac{AB}{DE} = \frac{AC}{DF}[/tex] = [tex]\frac{1}{2}[/tex] (corresponding sides are equal )
and
angle between corresponding side will also be same
therefore,
ΔABC ≅ ΔDEF (by SAS theorem )
Hence, ΔABC and ΔDEF are similar to each other by SAS similarity rule .
To know more about similarity of triangles here:
https://brainly.com/question/25882965
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