Part A
- Converse = "If corresponding angles are equal, then two lines are parallel"
- Result = True
Explanation:
Refer to the converse of the corresponding angles theorem. The original version is stated as part A, and the converse is marked in bold above.
Conditional statements are of the form "if this, then that". Symbolically we can use the template "If P, then Q". The P and Q are placeholders for logical statements.
The converse of "if P, then Q" is "If Q, then P". We swap the positions of P and Q. Do not negate either piece.
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Part B
- Converse = "If angle C is 70 degrees, then the sum of angles A and B is 110 degrees"
- Result = True
Explanation:
Recall that for any triangle, the three interior or inside angles always add to 180 degrees. In short: A+B+C = 180. If C = 70, then A+B = 180-C leads to A+B = 180-70 and A+B = 110. This process can be reversed.
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Part C
- Converse = "If two lines are not parallel, then alternate interior angles k and s are not equal"
- Result = True
Explanation:
For more information, check out the converse of the alternate interior angles theorem. The regular version of the theorem is "If two lines are parallel, then the alternate interior angles are congruent".
The converse of this theorem flips things to say: "If alternate interior angles are congruent, then the lines are parallel".
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Part D
- Converse = "If John loses his money, then he throws coins in the fountain"
- Result = False
Explanation:
Throwing coins in a fountain is one way to lose money, but there are other ways. He could drop a coin somewhere, or leave the coin somewhere he forgot.
In other words, just because he lost his money does not mean he threw a coin in the fountain.
