Answer:
Statement Reason
1. <R=<Q, AS=AT Given
2. <5=<6 Base <'s of isosceles triangles are =
3. <4, <5 are supplementary Exterior sides in opposite rays
and <6, <7 are supplementary
4. <4=<7 Two <'s supplementary to equal <'s are =
5. Triangle RAS congruent to AAS
Triangle QAT
6. RS=QT CPCTE
Explanation:
Statement
1. <R=<Q, AS=AT. This is given.
2. <5=<6, because base angles of isosceles triangles are congruent.
3. <4, <5 are supplementary and <6, <7 are supplementary, because they have exterior sides in opposite rays.
4. <4=<7, because two angles supplementary to equal angles are congruent
5. Triangle RAS congruent to Triangle QAT because Angle Angle Side (AAS)
6. RS=QT, because Congruent Parts in Congruent Triangles are equal (CPCTE)