Question

1. match one diagram and one notation to each term.
2. looking at the diagram below, label each statement to the right either true or false.

a) another name for line j is $overline{df}$
b) the intersection of plane m and $overline{bc}$ is point e.
c) points a, b, e and c are coplanar.
d) another name for plane m is plane bde.
e) points b, e and c are collinear.
f) points a, d and f are collinear.

Explanation:

Step1: Analyze line - naming

A line can be named by any two points on it. Since points D and F are on line j, another name for line j is $\overline{DF}$, so a) is TRUE.

Step2: Check plane - line intersection

The line $\overline{BC}$ does not intersect Plane M at Point E, so b) is FALSE.

Step3: Determine coplanarity

Point B is not on Plane M while A, E and C are on Plane M, so A, B, E and C are not coplanar, c) is FALSE.

Step4: Rename plane

Points B, D and E are on Plane M, so another name for Plane M is Plane BDE, d) is TRUE.

Step5: Check collinearity

Points B, E and C are on the same line (as $\overline{BC}$), so they are collinear, e) is TRUE.

Step6: Check collinearity

Points A, D and F are not on the same line, so they are not collinear, f) is FALSE.

Answer:

a) TRUE
b) FALSE
c) FALSE
d) TRUE
e) TRUE
f) FALSE