The corresponding angles between parallel lines and their common transversal are congruent
The other facts Jason can conclude are true are:
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
The reason why the above selected options are correct are:
The relationships between the lines Jason knows are:
Segment AK is perpendicular to KB: [tex]\underset{AK}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex]
Segment AK is parallel to EF: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex]
Segment AK is parallel to CB: [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex]
m∠DKF = 90°
The required information:
The facts that Jason can conclude are true
Method:
Find the other relationships between the lines based on the relationships Jason knows
Solution:
We have;
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
[tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{EF}{\leftrightarrow}[/tex], and [tex]\underset{AK}{\leftrightarrow}[/tex] ║ [tex]\underset{CB}{\leftrightarrow}[/tex], therefore, [tex]\mathbf{\underset{EF}{\leftrightarrow}}[/tex] ║ [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex]
The relationship, [tex]\underset{EF}{\leftrightarrow}[/tex] ⊥ [tex]\underset{KB}{\leftrightarrow}[/tex], gives m∠JFB = 90°
Therefore;
The correct options for the facts Jason can conclude are;
1) [tex]\mathbf{\underset{CB}{\leftrightarrow}}[/tex] ⊥ [tex]\mathbf{\underset{KB}{\leftrightarrow}}[/tex]
2) m∠JFB = 90°
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