Given that triangle ABC is congruent to triangle DEC, find the value of x. (Apex)
2 answers:
Answer:
x = 8
Step-by-step explanation:
In the figure attached ΔABC is similar to ΔCDE
By theorem of similarity of the triangles, corresponding sides of the similar triangles will be in the same ratio.
By cross multiplication
5(x + 1) = 3(2x -1)
5x + 5 = 6x - 3
5x - 6x + 5 = -3
-x + 5 = -3
-x = -3 - 5
-x = -8
x = 8
Therefore, x = 8 is the answer.
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From the given figure ,
RECA is a quadrilateral
RC divides it into two parts
From the triangles , ∆REC and ∆RAC
RE = RA (Given)
angle CRE = angle CRA (Given)
RC = RC (Common side)
Therefore, ∆REC is Congruent to ∆RAC
∆REC =~ ∆RAC by SAS Property
⇛CE = CA (Congruent parts in a congruent triangles)
Hence , Proved
<em>Additional</em><em> comment</em><em>:</em><em>-</em>
SAS property:-
"The two sides and included angle of one triangle are equal to the two sides and included angle then the two triangles are Congruent and this property is called SAS Property (Side -Angle-Side)
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