Question

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. (overline{dc}) is perpendicular to line (ell). 16. (overline{fb}) is perpendicular to line (n). 17. ∠fbj and ∠jba are complementary. 18. line (m) bisects ∠jch. 19. ∠abj and ∠dch are supplementary.

Explanation:

Step1: Check collinearity

Points A, F, and G do not lie on the same straight - line. So the statement "Points A, F, and G are collinear" is false.

Step2: Check supplementary angles

\(\angle DCJ\) and \(\angle DCH\) form a linear pair (a straight - line \(\overline{JH}\) with point C on it). Since the sum of angles in a linear pair is \(180^{\circ}\), \(\angle DCJ\) and \(\angle DCH\) are supplementary. This statement is true.

Step3: Check perpendicularity

\(\overline{DC}\) is not perpendicular to line \(\ell\) as there is no right - angle symbol indicating perpendicularity between them. This statement is false.

Step4: Check perpendicularity

\(\overline{FB}\) is perpendicular to line \(n\) as indicated by the right - angle symbol at the intersection. This statement is true.

Step5: Check complementary angles

\(\angle FBJ\) and \(\angle JBA\) form a right - angle (\(\angle FBA = 90^{\circ}\)). Since the sum of complementary angles is \(90^{\circ}\), \(\angle FBJ\) and \(\angle JBA\) are complementary. This statement is true.

Step6: Check angle bisection

Line \(m\) is perpendicular to line \(n\) at point C, and \(\angle JCH = 180^{\circ}\). Line \(m\) divides \(\angle JCH\) into two \(90^{\circ}\) angles. So line \(m\) bisects \(\angle JCH\). This statement is true.

Step7: Check supplementary angles

\(\angle ABJ=90^{\circ}\) and \(\angle DCH = 90^{\circ}\), and \(90^{\circ}+90^{\circ}=180^{\circ}\). So \(\angle ABJ\) and \(\angle DCH\) are supplementary. This statement is true.

Answer:

1. False
2. True
3. False
4. True
5. True
6. True
7. True