In this worksheet, we will practice constructing angle bisectors and perpendiculars from points outside straight lines.

**Q2: **

Draw any line segment from a point to a point and bisect it at the point . From , draw a line perpendicular to to a point . What can you say about the lengths of and ?

- A
- B
- C

**Q3: **

What does the following figure illustrate?

- Aa perpendicular from a point lying outside a straight line
- Ba bisector of an angle
- Ca straight line parallel to another line
- Da perpendicular to a straight line originating from it
- Ea bisector of a line segment

**Q4: **

What construction is illustrated below?

- Aa bisector of a line segment
- Ba bisector of an angle
- Ca straight line parallel to another line
- Da perpendicular from a point lying outside a straight line
- Ean angle congruent to another angle

**Q5: **

Draw a triangle in which , , and . Bisect with a line that intersects at the point . Measure the length of .

- A 4.2 cm
- B 3.9 cm
- C 3 cm
- D 2.4 cm

**Q6: **

Draw a triangle in which and . First, bisect at and at , then connect the points to draw . Using the drawing, determine the length of

**Q7: **

Draw the triangle , where , , and . Then draw a perpendicular line from to intersecting it at , and a perpendicular line from to intersecting it at . Use the ruler to find the lengths of and .

- A ,
- B ,
- C ,
- D ,

**Q8: **

Draw a triangle , in which , , and . Then draw a perpendicular line from to that intersects it at , draw another perpendicular line from to that intersects it at , and finally draw a perpendicular line from to that intersects it at . Use the ruler to find the lengths of , , and .

- A , ,
- B , ,
- C , ,
- D , ,

**Q10: **

What does the following figure illustrate?

- Aa perpendicular from a point lying outside a straight line
- Ba bisector of an angle
- Ca straight line parallel to another line
- Da perpendicular to a straight line originating from it
- Ea bisector of a line segment

**Q11: **

What construction is illustrated below?

- Aa bisector of a line segment
- Ba bisector of an angle
- Ca straight line parallel to another line
- Da perpendicular from a point lying outside a straight line
- Ean angle congruent to another angle

**Q12: **

Draw the triangle , where , , and . Then draw a perpendicular line from to intersecting it at , and a perpendicular line from to intersecting it at . Use the ruler to find the lengths of and .

- A ,
- B ,
- C ,
- D ,

**Q13: **

Draw a triangle , in which , , and . Then draw a perpendicular line from to that intersects it at , draw another perpendicular line from to that intersects it at , and finally draw a perpendicular line from to that intersects it at . Use the ruler to find the lengths of , , and .

- A , ,
- B , ,
- C , ,
- D , ,