Question

analyzing statements use the diagram shown at the right to determine whether the statement is true or false. (review 2.2) 46. points g, l, and j are collinear. 47. $overline{bc} perp overline{fg}$ 48. $angle ecb cong angle acd$ 49. $angle jhl$ and $angle jhf$ are complementary. 50. $overleftrightarrow{ak} perp overleftrightarrow{bd}$

Explanation:

Step1: Recall collinear - point definition

Collinear points lie on the same straight - line. Points G, L, and J do not lie on the same straight - line. So, the statement "Points G, L, and J are collinear" is false.

Step2: Recall perpendicular - line definition

$\overline{BC}$ and $\overline{FG}$ intersect at a right - angle (as indicated by the right - angle symbol at the intersection point). So, $\overline{BC}\perp\overline{FG}$ is true.

Step3: Recall vertical - angle property

$\angle ECB$ and $\angle ACD$ are vertical angles. Vertical angles are congruent. So, $\angle ECB\cong\angle ACD$ is true.

Step4: Recall complementary - angle definition

Complementary angles add up to 90 degrees. $\angle JHL$ and $\angle JHF$ form a right - angle at H, so $\angle JHL+\angle JHF = 90^{\circ}$. So, $\angle JHL$ and $\angle JHF$ are complementary is true.

Step5: Check perpendicular - line relationship

$\overleftrightarrow{AK}$ and $\overleftrightarrow{BD}$ do not intersect at a right - angle. So, $\overleftrightarrow{AK}\perp\overleftrightarrow{BD}$ is false.

Answer:

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