Question

example 3
a) write another name for ∠cbf.
b) name the sides of ∠ebd.
c) classify ∠abc.
d) give an example of an obtuse angle.
e) name two congruent angles.
f) name a perpendicular bisector.

Explanation:

Step1: Recall angle - naming and classification rules

Angles are named by the points on their rays with the vertex in the middle. Acute angles are less than 90°, right - angles are 90°, and obtuse angles are greater than 90° and less than 180°. Congruent angles have the same measure and a perpendicular bisector is a line that divides another line segment at a 90 - degree angle and into two equal parts.

Step2: Answer part a

$\angle CBF$ can also be named $\angle FBC$ since the vertex is $B$ and the rays are $\overrightarrow{BC}$ and $\overrightarrow{BF}$.

Step3: Answer part b

The sides of $\angle EBD$ are $\overrightarrow{BE}$ and $\overrightarrow{BD}$.

Step4: Answer part c

$\angle ABC$ is a right - angle as indicated by the right - angle symbol at $B$.

Step5: Answer part d

An example of an obtuse angle could be $\angle EBC$ since it is greater than 90° and less than 180°.

Step6: Answer part e

$\angle EBA$ and $\angle FBC$ could be congruent if they have the same measure (for example, if they are both 45°). Another pair could be $\angle ABD$ and $\angle DBC$ if they are both 45°.

Step7: Answer part f

If a line divides $\angle ABC$ (a right - angle) into two equal 45° angles, and is perpendicular to the line segment it intersects, a possible perpendicular bisector could be the line that divides $\angle ABC$ into two equal parts. For example, if there is a line $l$ passing through $B$ such that it divides $\angle ABC$ into two congruent 45° angles and is perpendicular to the line containing $AC$, then $l$ is a perpendicular bisector. But from the given rays, if we assume that the line perpendicular to the line containing $AC$ and passing through $B$ is considered, we can say that the line containing $BD$ (since $\angle ABC = 90^{\circ}$ and if $BD$ is perpendicular to the line containing $AC$) could be a perpendicular bisector in a context where it also bisects a line segment on the line containing $AC$.

Answer:

a) $\angle FBC$
b) $\overrightarrow{BE}$, $\overrightarrow{BD}$
c) Right - angle
d) $\angle EBC$
e) $\angle EBA$ and $\angle FBC$; $\angle ABD$ and $\angle DBC$
f) The line containing $BD$ (assuming it is perpendicular to the line containing $AC$ and bisects a relevant line segment on it)