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uranmaximum [27]
3 years ago
9

Is △DBE similar to △ABC ? If so, which postulate or theorem proves these two triangles are similar?

Mathematics
2 answers:
mash [69]3 years ago
6 0
DBE is similar to ABC by the SAS Similarity Theorem
Ipatiy [6.2K]3 years ago
5 0

Answer:

Step-by-step explanation:

In the given figure we have two triangles (One into another).

In triangle BDE,

DB=10\ cm

BE=16\ cm

In triangle ABC,

AB=BD+AD=10+15=25\ cm

BC=CE+EB=24+16=40\ cm

Now, in ΔABC and ΔBDE , we have

\angle{B}=\angle {B}                [Reflexive property]

\dfrac{BD}{AB}=\dfrac{10}{25}=\dfrac{2}{5}=\dfrac{16}{40}=\dfrac{BE}{CE}

By SAS Similarity Theorem ​,

ΔDBE ​ is similar to ​ ΔABC ​

  • SAS Similarity Theorem say that if two sides in a triangle are proportional to two sides in another triangle and the included angle in both are congruent then the two triangles are said to be  similar.

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