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The figure shows two parallel lines AB and DE cut by the transversals AE and BD:

Which statement best explains the relationship between Triangle ABC and Triangle EDC ?

The figure shows two parallel lines AB and DE cut by the transversals AE and BD Which statement best explains the relationship between Triangle ABC and Triangle class=

Respuesta :

kimberlybottch
I'm guessing it's the angles, for example: 3 is congruent to 4; and D is congruent to A, etc.

Answer: [tex]\triangle ABC\sim \triangle EDC[/tex]

That is, triangles ABC and EDC are similar.

Step-by-step explanation:

Given : [tex]AB\parallel DE[/tex]

AE and BD are the common transversal of the parallel lines AB and DE,

Then By the alternative interior angle theorem,

[tex]\angle BAC\cong \angle DEC[/tex]

And, [tex]\angle ABC\cong \angle EDC[/tex]

Thus, By AA similarity postulate,

[tex]\triangle ABC\sim \triangle EDC[/tex]

⇒ triangles ABC and EDC are similar.