contestada

Consider parallel lines cut by a transversal. Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Respuesta :

Answer:

Corresponding angle theorem, vertical angle theorem, and the transitive property of congruence.

Step-by-step explanation:

Considering a set of parallel lines cut by a transversal. (Refer the attached image).

Now that lines J and K are parallel, then by "corresponding angle theorem"

[tex]\angle 1=\angle 5[/tex]

By "vertical angle theorem"

[tex]\angle 5 = \angle 7[/tex]

Using, "transitive property of congruence"

[tex]\angle 1 = \angle 7[/tex]

And that is our required proof. In this whole proof we have used "corresponding angle theorem", "vertical angle theorem", and the "transitive property of congruence".

Ver imagen FelisFelis
MrRoyal

Angles between a transversal line and parallel lines are congruent based on vertical angle theorem, corresponding angles and transitive property.

I will use the attached figure to explain the congruence of the angles.

Corresponding Angles Theorem

From the attached figure, the following angles are congruent based on corresponding angle theorem

[tex]\angle 2 = \angle 6[/tex]            

[tex]\angle 1 = \angle 5[/tex]

[tex]\angle 4 = \angle 8[/tex]

[tex]\angle 3 = \angle 7[/tex]

Vertical Angle Theorem

From the attached figure, the following angles are congruent based on vertical angle theorems

[tex]\angle 2 = \angle 3[/tex]            

[tex]\angle 1 = \angle 4[/tex]

[tex]\angle 5 = \angle 8[/tex]

[tex]\angle 6 = \angle 7[/tex]

Transitive Property

From the attached figure, the following angles are congruent based on transitive property

[tex]\angle 1 = \angle 7[/tex]

[tex]\angle 4 = \angle 6[/tex]

[tex]\angle 5 = \angle 3[/tex]            

[tex]\angle 2 = \angle 8[/tex]

Read more about angles between a transversal and parallel lines at:

https://brainly.com/question/16967505

Ver imagen MrRoyal

Otras preguntas

Q&A Education