Points, Lines, Planes and Angles

For the following figure, name the graph of the given equation or inequality $\left|x\right|\mathbf{\ge }\mathbf{0}$.

For the following figure, name the graph of the given equation or inequality $\left|x\right|\mathbf{=}\mathbf{0}$.

a. On $\overrightarrow{\mathbf{A}\mathbf{B}}$, how many points are there whose distance from point A is 3 cm?

b. On $\overleftrightarrow{\mathbf{A}\mathbf{B}}$, how many points are there whose distance from point A is 3 cm?

On $\overrightarrow{\mathbf{A}\mathbf{B}}$, how many points are there whose distance from point $\mathit{B}$ is 3 cm?

The ruler postulate suggests that there are many ways to assign coordinates to a line. The Fahrenheit and Celsius temperature scales on a thermometer indicate two such ways of assigning coordinates. A Fahrenheit temperature of $\mathbf{32}\mathbf{°}$ corresponds to a Celsius temperature of ${\mathbf{0}}^{\mathbf{\circ }}$. The formula, or rule for converting a Fahrenheit temperature F into a Celsius temperature C is $\mathit{C}\mathbf{=}\frac{\mathbf{5}}{\mathbf{9}}\left(F-32\right)$.

a. What Celsius temperatures corresponds to Fahrenheit temperature of ${\mathbf{212}}^{\mathbf{\circ }}\mathbf{,}\mathbf{98}{\mathbf{.6}}^{\mathbf{\circ }}$?

b. Solve the equation above for F to obtain a rule for converting Celsius temperature to Fahrenheit temperatures.

c. What Fahrenheit temperatures correspond to Celsius temperatures of $\mathbf{-}{\mathbf{40}}^{\mathbf{\circ }}\mathbf{,}{\mathbf{2000}}^{\mathbf{\circ }}$?

For the following figure, name the vertex and sides of the angle $\angle 4$.

For the following figure, name the vertex and sides of the angle $\angle 1$.

For the following figure, name the vertex and sides of the angle $\angle 6$.

For the following figure, name the angles adjacent to $\angle 6$.

For the following figure, name three angles that have B as the vertex.

For the following figure, name the angles have  as the vertex.

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle 1$
  

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle 2$
  

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle EDB$
  

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle CDB$
  

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle ADC$
  

State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure.

• $\angle ADE$
  

Complete. $m\angle 7+m\angle 6=m\angle ?$

Complete.

If $\overline{DB}$ bisects $\angle CDA$ then $\angle ?\cong \angle ?$.

State the measure of each angle.

• $\angle BOC$
  

State the measure of each angle.

• $\angle GOH$
  

State the measure of each angle.

• $\angle FOG$
  

Complete. $m\angle 6+m\angle 5=m\angle ?$

Complete. $m\angle 2+m\angle 3=?$

State the measure of each angle.

• $\angle COF$
  

State the measure of each angle.

• $\angle GOB$
  

State the measure of each angle.

• $\angle HOA$
  

Name four angles that are adjacent to $\angle FOG$.

What ray bisects which two angles?

Name a pair of congruent:

a. acute angles

b. right angles

c. obtuse angles

Study a corner of your classroom where two walls and the ceiling meet. How many right angles can you see at the corner?

Draw an angle, $\angle AOB$, on a sheet of paper. Fold the paper so that $\overline{OA}$ falls on $\overline{OB}$. Lay the paper flat and call the fold line $\overline{OK}$. How is $\overline{OK}$ related to $\angle AOB$? Explain.

Given the diagram, state whether you can reach the conclusion shown.

$m\angle FOB=50°$

Given the diagram, state whether you can reach the conclusion shown.

$m\angle AOC=90$

Given the diagram, state whether you can reach the conclusion shown.

$m\angle DOC=180$

Given the diagram, state whether you can reach the conclusion shown.

$AO=OB$

Given the diagram, state whether you can reach the conclusion shown.

$\angle AOC\cong \angle BOC$

Given the diagram, state whether you can reach the conclusion shown.

$m\angle AOF\simeq 130$

Given the diagram, state whether you can reach the conclusion shown.

Points E, O, and F are collinear.

Given the diagram, state whether you can reach the conclusion shown.

Point C is in the interior of $\angle AOF$.

Given the diagram, state whether you can reach the conclusion shown.

$\angle AOE$ and $\angle AOD$ are adjacent angles.

Given the diagram, state whether you can reach the conclusion shown.

$\angle AOB$is a straight angle.

Given the diagram, state whether you can reach the conclusion shown.

$\overrightarrow{OA}$ and $\overrightarrow{OB}$ are opposite rays.

Name the vertex and sides of $\angle 5$.

Name all angles adjacent to $\angle ADE$.

State another name for the angle.

$\angle 1$

State another name for the angle.

$\angle 3$

State another name for the angle.

$\angle 5$

State another name for the angle.

$\angle ALD$

State another name for the angle.

$\angle AST$