Chapter 2: Q2. (page 68)
Provide a counter example to disprove the statement:
If , then .
Short Answer
The example that disproves the statement is as it satisfies the first statement but does not satisfy the second condition.
Chapter 2: Q2. (page 68)
Provide a counter example to disprove the statement:
If , then .
The example that disproves the statement is as it satisfies the first statement but does not satisfy the second condition.
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Get started for freeTell whether each statement is true or false. Then write the converse and tell whether it is true or false.
if .
State the converse of each conditional. Is the converse true or false?
If , then
.
Justify each statement with a property from algebra or property of congruence .
Prove the following statement by filling in the blanks.
If A and B have coordinated a and b, with , and the midpoint M of has coordinate x, then prove .
Proof:
Statement | Reasons |
1. A, M, and B have coordinated a, x, and b respectively; . | 1. ? |
2. | 2. ? |
3. M is the midpoint of . | 3. ? |
4. , or | 4. ? |
5. | 5. ? |
6. ? | 6. ? |
7. | 7. ? |
Consider the following statements:
Reflexive Property: Robot A is as rusty as itself.
Symmetric Property: If Robot A is as rusty as Robot B, then Robot B is as rusty as Robot A.
Transitive Property: If Robot A is as rusty as Robot B and Robot B is as rusty as Robot C, then Robot A is as rusty as Robot C.
A relation such as “is as rusty as” that is reflexive, symmetric, and transitive is an equivalence relation. Which of the following are equivalence relations?
a. Is rustier than
b. Has the same length as
c. Is opposite (for rays)
d. Is coplanar with (for lines)
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