Answer :
The angle formed at corresponding locations between lines [tex]\overline{PR}[/tex] and [tex]\overline {TQ}[/tex]
and the common transversal [tex]\overline {WV}[/tex] are corresponding angles.
The statements that support Susan's predictions are;
- m∠PRV and m∠TQR are corresponding angles
- m∠PRV = 130° = m∠TQR
- m∠PRV ≅ m∠TQR by congruency definition
- [tex]\overline{PR} \cong \overline {TQ}[/tex] by corresponding angles theorem
Reason:
The given measures of ∠TQR are;
In figure 1, m∠TQR = 145°
In figure 2, m∠TQR = 140°
In figure 3, m∠TQR = 135°
Therefore, we have the following sequence;
145°, 140°, 135°
From the above sequence, we have that each subsequent term, is less
than the previous one by 5 degrees, therefore on figure 4, we have;
Figure 4, m∠TQR = 135° - 5° = 130°
Therefore, on figure 4, we get;
m∠PRV and m∠TQR are corresponding angles
m∠PRV = 130° = m∠TQR
Which gives;
m∠PRV ≅ m∠TQR by definition of congruency
Therefore;
[tex]\overline{PR} \cong \overline {TQ}[/tex] by corresponding angles theorem.
Corresponding angles theorem states that if two lines that are parallel have
a common transversal cutting both lines, the corresponding angles formed
are congruent.
Therefore, the statements that support Susan's prediction are;
On figure 4;
- m∠PRV and m∠TQR are corresponding angles
- m∠PRV = 130° = m∠TQR
- m∠PRV ≅ m∠TQR by definition
- [tex]\overline{PR} \cong \overline {TQ}[/tex] by corresponding angles theorem
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