The option that shows the triangles that are congruent and the reason that justifies that congruence is: b. [tex]\triangle ABC \cong \triangle EDF $ by$ ASA[/tex]
Recall:
According to the Angle-Side-Angle Congruence Theorem (ASA), two triangles are congruent to each other if:
- Two angles in one triangle equals two corresponding angles in the other one
- An included side that lies between the two angles of one triangle is congruent to the included side of the other triangle.
Lets analyze the diagram given:
- Note: arrangement of the letters that form a triangle must be taken into consideration.
[tex]\angle A = \angle E = 40^{\circ} $ (congruent $ angles) \\\\ \\\angle C = \angle F = 127^{\circ} $ (congruent $ angles)[/tex]
[tex]AC = 2 - 0 = 2 $ units\\\\EF = 4 - 2 = 2 $ units[/tex]
[tex]AC = EF[/tex] (included side)
Two angles and one included side in [tex]\triangle ABC[/tex] is congruent to two angles and one included side in [tex]\triangle EDF[/tex]
Therefore, [tex]\triangle ABC \cong \triangle EDF $ by$ ASA[/tex]
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