Answer:
Given: [tex]r || s[/tex] and q is a transversal.
Alternative Interior Angle states that a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal are equal.
By alternative interior angle;
[tex]\angle 3 \cong \angle 6[/tex]
Definition of Congruent angles are angles that have the same degree of measurement.
Therefore, [tex]m\angle 3 = m\angle 6[/tex] [By definition of Congruent] .....[1]
Linear Pair states that a pair of adjacent angles formed when two lines are intersect.
therefore, [tex]\angle 4[/tex] and [tex]\angle 3[/tex] are a linear pair. [by definition of linear pair]
Two angles of linear pairs are always supplementary , which means their measure are add up to 180 degree.
By the definition of supplementary angles, [tex]m\angle 4 + m\angle 3 = 180^{\circ}[/tex] .....[2]
Substitute equation [1] in [2] we get,
[tex]m\angle 4 +m\angle 6 =180^{\circ}[/tex]
By the definition of supplementary angles,
[tex]\angle 4[/tex] is supplementary to [tex] \angle 6[/tex] Hence proved!
Answer:
Step-by-step explanation:
Given: r || s and q is a transversal .
To Prove: ∠4 is supplementary to ∠6 .
Proof: It is given that r is parallel to s and q is a transversal, then
∠3 ≅ ∠6 by the (Alternate interior angles).
Therefore, m∠3 = m∠6 by the definition of congruency.
We also know that, by definition, ∠4 and ∠3 are a linear pair, so they are supplementary by the linear pair postulate.
By the definition of supplementary angles, m∠4 + m∠3 = 180°. (1)
Now, Using substitution,
We can replace m∠3 with m∠6 in equation (1) to get m∠4 + m∠6 = 180°. Therefore, by the definition of supplementary angles, ∠4 is supplementary to ∠6.
Hence proved.
