The missing statement for step 6 is C. m∠SQV + m∠SQT = 180°, as it represents the Same Side Interior Angle Theorem which states that same side interior angles add up to 180 degrees.
The missing statement for step 6 in the sequence provided by the student involves understanding the Same Side Interior Angle Theorem.
This theorem states that if two parallel lines are cut by a transversal, the same side interior angles are supplementary, meaning their measures add up to 180 degrees.
Based on the given options, the correct statement that corresponds to the Same Side Interior Angle Theorem is C. m∠SQV + m∠SQT = 180°.
This statement follows from the theorem because ∠SQV and ∠SQT are on the same side of the transversal and are interior to the two lines cut by the transversal, which by the theorem, should add to 180 degrees.
The probable question may be:
5. m∠SQV + m∠VQT = 180° Substituion property of equality
6. ____________ Same side interior angle theorem
7. m∠SQV + m∠SQT = m∠VQT+ m∠ZRS Substituion property of equality
8. m∠SQV + m∠VQT - m∠VQT = m∠VQT + m∠ZRS - m∠VQT Substraction property of equality
m∠SQV = m∠ZRS
m∠SQV≅m∠ZRS Definition of congruency
What is the missing statement for step 6?
A. m∠SQV + m∠VQT = 180°
B. m∠SQV + m∠SQT = m∠VQT
C. m∠SQV + m∠SQT = 180°
D. m∠VQT + m∠ZRS = 180°