(1) part a: a circle is the set of all points that are the same distance from one given point. find an example that contradicts this definition. how would you change the definition to make it more accurate?
part b: give an example of an undefined term and how it relates to a circle.
(2) isaac will be constructing congruent segments with a compass and straightedge, while micah will be constructing a segment bisector with a compass and straightedge. describe the similarities and differences between their construction steps.
(3) describe at least two differences between constructing an inscribed regular hexagon and constructing an inscribed square.
(4) michael and derrick each completed a separate proof to show that corresponding angles akg and elk are congruent. who completed the proof incorrectly? explain.
line ab is parallel to ef, transversal gj crosses line ab at k and crosses line ef at l.
michael's proof
statement justification
1. line ab ∥ line ef with transversal segment gj 1. given
2. angle akg is congruent to angle akl 2. vertical angles theorem
3. angle bkl is congruent to angle elk 3. alternate interior angles theorem
4. angle akg is congruent to angle elk 4. transitive property
derrick's proof
statement justification
1. line ab ∥ line ef with transversal segment gj 1. given
2. angle akg is congruent to angle bkl 2. vertical angles theorem
3. angle bkl is congruent to angle elk 3. alternate interior angles theorem
4. angle akg is congruent to angle elk 4. transitive property