1) Match the following parts of the proof:
a) diagram
b) Column with specific information to the problem written in deductive order
c) Given and Prove statement that sets up the start and finish of a proof.
d) Column with allowed assumptions, definitions, postulates, theorems or algebraic properties.
Since we know that \(\angle 1\cong\angle 2\), then \(m\angle 1 = m\angle 2\) because congruent angles have the ____________ ____________. We are given that \(m\angle 1 = 70^{\circ}\) so \(m\angle 2 = 70^{\circ}\) by the
________________ _____________. Using angle addition \(m\angle 1 + m\angle 2 = m\angle\)______________. So, \(m\angle ABE = 70^{\circ} + 70^{\circ}\) = ____________ using substitution and addition. \(\angle ABE\) and \(\angle\)________________ are a _______________ pair. Linear pairs are ____________________. So, \(m\angle ABE + m\angle 3\) = ____________ because supplementary angles add up to \(180^{\circ}\). Using substitution _____________ + \(m\angle 3 = 180^{\circ}\). Therefore, \(m\angle 3 =\)____________ by __________________.
________________ _____________. Using angle addition \(m\angle 1 + m\angle 2 = m\angle\)______________. So, \(m\angle ABE = 70^{\circ} + 70^{\circ}\) = ____________ using substitution and addition. \(\angle ABE\) and \(\angle\)________________ are a _______________ pair. Linear pairs are ____________________. So, \(m\angle ABE + m\angle 3\) = ____________ because supplementary angles add up to \(180^{\circ}\). Using substitution _____________ + \(m\angle 3 = 180^{\circ}\). Therefore, \(m\angle 3 =\)____________ by __________________.
Statements (Claims) |
Reasons (Evidence) |
1. \(FI = 5\) |
1. \(\) |
2. \(I\) is midpoint of \(\overline{FV}\) |
2. \(\) |
3. \(\overline{FI}\cong\overline{IV}\) |
3. \(\) |
4. \(FI = IV\) |
4. If congruent segments, then equal length |
5. \(IV = \)_____ |
5. Substitution |
6. \(FV = FI + IV\) |
6. \(\) |
7. \(FV = 5 + 5\) |
7. |
8. |
8. Addition |
9. \(V\) is midpoint of \(\overline{FE}\) |
9. \(\) |
10. \(\overline{FV}\cong\overline{VE}\) |
10. \(\) |
11. \(FV = VE\) |
11. |
12. \(VE = 10\) |
12. |
Review
15) Given midpoint \(M (-1, 9)\) of \(\overline{AP}\). If \(P (-7, -1)\), what are the coordinates of \(A\)?
15) Given midpoint \(M (-1, 9)\) of \(\overline{AP}\). If \(P (-7, -1)\), what are the coordinates of \(A\)?