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In the figure,(p)parallel(q) and (r)pparallel(s). Match each pair of congruent angles with the reason for their congruency.

In the figurepparallelq and rpparallels Match each pair of congruent angles with the reason for their congruency class=
In the figurepparallelq and rpparallels Match each pair of congruent angles with the reason for their congruency class=

Respuesta :

Tyrant4life

Answer:

∠1≅∠5 by Corresponding angles for parallel line p and q cut by traversal r

∠5≅∠13 by Corresponding angles for parallel line r and s cut by traversal q

∠10≅∠14 by Corresponding angles for parallel line p and q cut by traversal s

∠13≅∠16 by Vertical angles theorem

akposevictor

The given pairs of congruent angles can be matched with their reasons as follows:

  • [tex]5 \angle \cong \angle 13[/tex] is: corresponding angles for lines r and s that is cut by traversal q

  • [tex]10 \angle \cong \angle 14[/tex] is: corresponding angles for lines p and q that is cut by traversal s

  • [tex]13 \angle \cong \angle 16[/tex] is:  vertical angles theorem.

  • [tex]1 \angle \cong \angle 5[/tex] is: corresponding angles for lines p and q that is cut by traversal r.

Given:

[tex]r \parallel s\\\\p \parallel q[/tex]

From the image,

1. [tex]\angle 5 $ and \angle 13[/tex] share the same corner along transversal q that cuts across lines r and s. Hence, both angles correspond to each other.

  • The reason for [tex]5 \angle \cong \angle 13[/tex] is: corresponding angles for lines r and s that is cut by traversal q

2. [tex]\angle 10 $ and \angle 14[/tex] share the same corner along transversal s that cuts across lines p and q. Hence, both angles correspond to each other.

  • The reason for [tex]10 \angle \cong \angle 14[/tex] is: corresponding angles for lines p and q that is cut by traversal s

3. [tex]\angle 13 $ and \angle 16[/tex] share the same vertex angle and are just directly opposite each other. Thus, they are vertically opposite each other and are therefore equal by the vertical angles theorem.

  • The reason for [tex]13 \angle \cong \angle 16[/tex] is:  vertical angles theorem.

4. [tex]\angle 1 $ and \angle 5[/tex] share the same corner along transversal r that cuts across lines p and q. Hence, both angles correspond to each other.

  • The reason for [tex]1 \angle \cong \angle 5[/tex] is: corresponding angles for lines p and q that is cut by traversal r.

In summary, the given pairs of congruent angles can be matched with their reasons as follows:

  • [tex]5 \angle \cong \angle 13[/tex] is: corresponding angles for lines r and s that is cut by traversal q

  • [tex]10 \angle \cong \angle 14[/tex] is: corresponding angles for lines p and q that is cut by traversal s

  • [tex]13 \angle \cong \angle 16[/tex] is:  vertical angles theorem.

  • [tex]1 \angle \cong \angle 5[/tex] is: corresponding angles for lines p and q that is cut by traversal r.

Learn more here:

https://brainly.com/question/19107710

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