Chapter 2: Q10. (page 57)
Name the definition or state the theorem that justifies the statement about the diagram.
If , then .
The used definition is the definition of perpendicular lines.
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Provide a counterexample to show that each statement is false.
Statement: If a four-sided figure has four congruent sides, then it has four right angles.
Justify each statement with a property from algebra or property of congruence.
If ,and then .
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)
Justify each statement with a property from algebra or property of congruence.
If then .
Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If , then .
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