Question

problem 4 constructing the angle bisector
got it? draw obtuse ∠xyz. then construct its bisector (overrightarrow{yp}).

1. obtuse ∠xyz is drawn in the box at the right. complete the flowchart and do each step of the construction.

step 1 put the compass point on vertex. draw an arc that intersects the sides of ∠xyz. label the points of intersection a and b.
step 2 put the compass point on point a and draw an arc. with the same / a different compass - setting, draw an arc using point b. be sure the arcs intersect. label the point where the two arcs intersect p.
step 3 draw
lesson check - do you understand?
vocabulary what two tools do you use to make constructions?
draw a line from each task in column a to the tool used in column b.
column a

1. measure lines
2. measure angles
3. construct arcs
4. construct lines

column b
compass
protractor
ruler
straightedge
math success
check off the vocabulary words that you understand.
straightedge compass construction perpendicular bisector
rate how well you can construct angles and bisectors.
0 2 4 6 8 10

Explanation:

Step1: Identify construction tools

The two main tools for geometric constructions are compass and straight - edge.

Step2: Match tasks with tools

1. measure lines - ruler (a type of straight - edge for measuring lengths)
2. measure angles - protractor
3. construct arcs - compass
4. construct lines - straightedge

For constructing the angle bisector in the first part:

Step1: Place compass on vertex

Put the compass point on vertex $Y$. Draw an arc that intersects the sides of $\angle XYZ$ at points $A$ and $B$.

Step2: Draw intersecting arcs

Put the compass point on point $A$ and draw an arc. With the same compass setting, draw an arc using point $B$. Let the intersection of these two arcs be point $P$.

Step3: Draw the bisector

Draw ray $\overrightarrow{YP}$. This ray is the angle - bisector of $\angle XYZ$.

Answer:

The two tools used for constructions are compass and straight - edge.

1. measure lines - ruler
2. measure angles - protractor
3. construct arcs - compass
4. construct lines - straightedge

For constructing the angle bisector of $\angle XYZ$, draw ray $\overrightarrow{YP}$ as described above.