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Given below are measurements of some par...

Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by using `SAS` congruence rule. If the triangles are congruent, write them in symbolic form.
`/_\ABC` `/_\DEF`
`(a) AB = 7 cm, BC = 5 cm, /_B = 50^@ ` `DE = 5 cm, EF = 7 cm, /_E = 50^@`
`(b) AB = 4.5 cm, AC = 4 cm, /_A = 60^@``DE = 4 cm, FD = 4.5 cm, /_D = 55^@`
`(c) BC = 6 cm, AC = 4 cm, /_B = 35^@` `DF = 4 cm, EF = 6 cm, /_E = 35^@`

Text Solution

Verified by Experts

`(a)` Here, `AB = EF ( = 7 cm), BC = DE ( = 5 cm)` and included `/_B =` included `/_E ( = 50^@)`. Also, `A harr F B harr E` and `C harr D`. Therefore, `/_\ABC cong /_\FED` (By `SAS` congruence rule)
`(b)` Here, `AB = FD` and `AC = DE`
But included `/_A ne` included `/_D`. So, we cannot say that the triangles are congruent.
`(c)` Here, `BC = EF, AC = DF ` and `/_B = /_E`.
But `/_B` is not the included angle between the sides `AC` and `BC`.
Similarly, `/_E` is not the included angle between the sides `EF` and `DF`.
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