Question

1. error analysis what is wrong with the statement? the statements \i eat cereal only if it is morning\ and \if i eat cereal, then it is morning\ are not equivalent. check tell whether the statement is a biconditional. 3. i will work after school only if i have the time. 4. an angle is called a right - angle if and only if it measures 90°. 5. two segments are congruent if and only if they have the same length. rewrite the biconditional statement as a conditional statement and its converse. 6. the ceiling fan runs if and only if the light switch is on. 7. you scored a touchdown if and only if the football crossed the goal line. 8. the expression 3x + 4 is equal to 10 if and only if x is 2. windows decide whether the statement about the window shown is true. explain your answer using the definitions you have learned. 9. the points d, e, and f are collinear. 10. m∠cba = 90° 11. ∠dba and ∠ebc are not complementary. 12. de⊥ac practice and applications perpendicular lines use the diagram to determine whether the statement is true or false. 13. points a, f, and g are collinear. 14. ∠dcj and ∠dch are supplementary. 15. dc is perpendicular to line l. 16. fb is perpendicular to line m. 17. ∠fbj and ∠jba are complementary. 18. line m bisects ∠jch. 19. ∠abj and ∠dch are supplementary.

Explanation:

1. For the error - analysis question: "I eat cereal only if it is morning" means that cereal - eating is restricted to the morning, i.e., if cereal is eaten, then it is morning. "If I eat cereal, then it is morning" is the same logical statement. So, the original claim that they are not equivalent is wrong.
2. For question 3: It is not a biconditional. A biconditional is of the form "p if and only if q". Here, it is just a conditional "I will work after school only if I have the time", which means if I work after school, then I have the time.
3. For question 4: It is a biconditional. It can be written as a conditional "If an angle is a right - angle, then it measures 90°" and its converse "If an angle measures 90°, then it is a right - angle".
4. For question 5: It is a biconditional. Conditional: "If two segments are congruent, then they have the same length". Converse: "If two segments have the same length, then they are congruent".
5. For question 6: Conditional: "If the ceiling fan runs, then the light switch is on". Converse: "If the light switch is on, then the ceiling fan runs".
6. For question 7: Conditional: "If you scored a touchdown, then the football crossed the goal line". Converse: "If the football crossed the goal line, then you scored a touchdown".
7. For question 8: Conditional: "If the expression 3x + 4 is equal to 10, then x is 2". Converse: "If x is 2, then the expression 3x + 4 is equal to 10".
8. For questions 9 - 12 (window - related): Without seeing the window, we assume based on definitions. Collinear points lie on the same line. Complementary angles add up to 90°. Perpendicular lines form 90° angles.
9. For questions 13 - 19 (perpendicular lines and angle - related): Use the definitions of collinear points (points on the same line), supplementary angles (angles that add up to 180°), perpendicular lines (lines that form 90° angles), and angle - bisectors (a line that divides an angle into two equal parts).

Answer:

1. The statement in the error - analysis is wrong. They are equivalent.
2. 3. Not a biconditional.
3. 4. Biconditional.
4. 5. Biconditional.
5. 6. Conditional: If the ceiling fan runs, then the light switch is on. Converse: If the light switch is on, then the ceiling fan runs.
6. 7. Conditional: If you scored a touchdown, then the football crossed the goal line. Converse: If the football crossed the goal line, then you scored a touchdown.
7. 8. Conditional: If the expression 3x + 4 is equal to 10, then x is 2. Converse: If x is 2, then the expression 3x + 4 is equal to 10.
8. 9 - 12: Answers depend on the window diagram (not shown).
9. 13 - 19: Answers depend on the given diagram.