Question

geometry with trigonometry chapter 1 review 1. use the diagram to answer the following questions: a. name a point on line m. b. name a ray with an initial point a. c. name the intersection of line m and line p. d. what is another name for plane n? (hint: use 3 triangular letters) e. are ∠pcb and ∠bcd complementary? why/why not? f. are ∠pcb and ∠bcd adjacent? why/why not? g. is ∠pcb≅∠bcd? why/why not? h. are points a, b, and e collinear? i. does $overline{cd}$ intersect with $overline{bc}$? if so, what’s the intersection? j. another name for line m is _. k. b is between what 2 points? l. what of the following can be measured? $overline{bc}$, f, $overline{cd}$, $overline{ae}$ 2. which conclusion(s) can you make based on the following diagram? a. $overline{ab}=overline{bc}$ b. $ab = bc$ c. $overline{ab}congoverline{bc}$ d. $abcong bc$ e. $ab + bc=ac$ f. b is the midpoint

Explanation:

Step1: Analyze part a

A point on line $m$ is $B$.

Step2: Analyze part b

A ray with initial - point $A$ is $\overrightarrow{AB}$.

Step3: Analyze part c

The intersection of line $m$ and line $p$ is point $C$.

Step4: Analyze part d

Another name for Plane $N$ using 3 non - collinear points can be Plane $FBC$.

Step5: Analyze part e

$\angle PCB$ and $\angle BCD$ are not complementary because their sum is not $90^{\circ}$. There is no indication that they form a right - angle.

Step6: Analyze part f

$\angle PCB$ and $\angle BCD$ are adjacent because they have a common side $\overrightarrow{BC}$, a common vertex $C$, and no overlapping interior points.

Step7: Analyze part g

There is no information to suggest that $\angle PCB\cong\angle BCD$. We don't know if they have equal measures.

Step8: Analyze part h

Points $A$, $B$, and $E$ are not collinear as they do not lie on the same straight line.

Step9: Analyze part i

$\overrightarrow{CD}$ and $\overrightarrow{BC}$ do not intersect. A ray has a start - point and extends infinitely in one direction, and these two rays do not cross paths.

Step10: Analyze part j

Another name for line $m$ is line $BC$.

Step11: Analyze part k

$B$ is between $A$ and $C$.

Step12: Analyze part l

Line segments $\overline{BC}$, $\overline{CD}$, and $\overline{AE}$ can be measured as they have two endpoints. A point $F$ cannot be measured.

Step13: Analyze part 2

Given points $A$, $B$, and $C$ on a line, we know that $AB + BC=AC$ (by the segment - addition postulate). There is no indication that $AB = BC$ or $\overline{AB}\cong\overline{BC}$.

Answer:

1.
a. $B$
b. $\overrightarrow{AB}$
c. $C$
d. Plane $FBC$
e. No, their sum is not $90^{\circ}$.
f. Yes, they have a common side, common vertex and non - overlapping interiors.
g. No, no information about equal measures.
h. No, they are not on the same line.
i. No
j. line $BC$
k. $A$ and $C$
l. $\overline{BC}$, $\overline{CD}$, $\overline{AE}$

1. e. $AB + BC = AC$