Worksheet: Geometric Constructions

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

Q1:

What does the following figure illustrate?

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

Q2:

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

  • A 𝐴 𝐵 > 𝐴 𝐶
  • B 𝐴 𝐵 < 𝐴 𝐶
  • C 𝐴 𝐵 = 𝐴 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 𝐴 𝐵 𝐶 in which 𝐴 𝐵 = 3 c m , 𝐵 𝐶 = 4 c m , and 𝐴 𝐶 = 5 c m . Bisect 𝐵 with a line that intersects 𝐴 𝐶 at the point 𝐷 . Measure the length of 𝐵 𝐷 .

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

Q6:

Draw a triangle 𝐴 𝐵 𝐶 in which 𝐴 𝐵 = 𝐴 𝐶 = 1 2 c m and 𝐵 𝐶 = 1 5 c m . First, bisect 𝐴 𝐵 at 𝐷 and 𝐴 𝐶 at 𝐸 , then connect the points to draw 𝐷 𝐸 . Using the drawing, determine the length of 𝐷 𝐸

Q7:

Draw the triangle 𝐴 𝐵 𝐶 , where 𝐴 𝐵 = 6 . 2 c m , 𝐵 𝐶 = 1 2 c m , and 𝐴 𝐶 = 1 3 c m . Then draw a perpendicular line from 𝐴 to 𝐵 𝐶 intersecting it at 𝑋 , and a perpendicular line from 𝐵 to 𝐴 𝐶 intersecting it at 𝑌 . Use the ruler to find the lengths of 𝐴 𝑋 and 𝐵 𝑌 .

  • A 𝐴 𝑋 5 . 7 c m , 𝐵 𝑌 5 . 7 c m
  • B 𝐴 𝑋 6 . 2 c m , 𝐵 𝑌 5 . 2 c m
  • C 𝐴 𝑋 5 . 7 c m , 𝐵 𝑌 5 . 2 c m
  • D 𝐴 𝑋 6 . 2 c m , 𝐵 𝑌 5 . 7 c m

Q8:

Draw a triangle 𝐴 𝐵 𝐶 , in which 𝐴 𝐵 = 8 c m , 𝐵 𝐶 = 6 c m , and 𝑚 𝐵 = 1 2 0 . Then draw a perpendicular line from 𝐴 to 𝐵 𝐶 that intersects it at 𝑋 , draw another perpendicular line from 𝐵 to 𝐴 𝐶 that intersects it at 𝑌 , and finally draw a perpendicular line from 𝐶 to 𝐴 𝐵 that intersects it at 𝑍 . Use the ruler to find the lengths of 𝐴 𝑋 , 𝐵 𝑌 , and 𝐶 𝑍 .

  • A 𝐴 𝑋 6 . 4 c m , 𝐵 𝑌 3 . 4 c m , 𝐶 𝑍 4 . 7 c m
  • B 𝐴 𝑋 6 . 9 c m , 𝐵 𝑌 2 . 9 c m , 𝐶 𝑍 4 . 7 c m
  • C 𝐴 𝑋 6 . 4 c m , 𝐵 𝑌 2 . 9 c m , 𝐶 𝑍 5 . 2 c m
  • D 𝐴 𝑋 6 . 9 c m , 𝐵 𝑌 3 . 4 c m , 𝐶 𝑍 5 . 2 c m

Q9:

What does the following figure illustrate?

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

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 𝐴 𝐵 𝐶 , where 𝐴 𝐵 = 5 . 8 c m , 𝐵 𝐶 = 1 5 c m , and 𝐴 𝐶 = 1 6 c m . Then draw a perpendicular line from 𝐴 to 𝐵 𝐶 intersecting it at 𝑋 , and a perpendicular line from 𝐵 to 𝐴 𝐶 intersecting it at 𝑌 . Use the ruler to find the lengths of 𝐴 𝑋 and 𝐵 𝑌 .

  • A 𝐴 𝑋 5 . 3 c m , 𝐵 𝑌 5 . 4 c m
  • B 𝐴 𝑋 5 . 8 c m , 𝐵 𝑌 4 . 9 c m
  • C 𝐴 𝑋 5 . 3 c m , 𝐵 𝑌 4 . 9 c m
  • D 𝐴 𝑋 5 . 8 c m , 𝐵 𝑌 5 . 4 c m

Q13:

Draw a triangle 𝐴 𝐵 𝐶 , in which 𝐴 𝐵 = 5 c m , 𝐵 𝐶 = 7 c m , and 𝑚 𝐵 = 1 2 0 . Then draw a perpendicular line from 𝐴 to 𝐵 𝐶 that intersects it at 𝑋 , draw another perpendicular line from 𝐵 to 𝐴 𝐶 that intersects it at 𝑌 , and finally draw a perpendicular line from 𝐶 to 𝐴 𝐵 that intersects it at 𝑍 . Use the ruler to find the lengths of 𝐴 𝑋 , 𝐵 𝑌 , and 𝐶 𝑍 .

  • A 𝐴 𝑋 3 . 8 c m , 𝐵 𝑌 2 . 9 c m , 𝐶 𝑍 5 . 6 c m
  • B 𝐴 𝑋 4 . 3 c m , 𝐵 𝑌 2 . 4 c m , 𝐶 𝑍 5 . 6 c m
  • C 𝐴 𝑋 3 . 8 c m , 𝐵 𝑌 2 . 4 c m , 𝐶 𝑍 6 . 1 c m
  • D 𝐴 𝑋 4 . 3 c m , 𝐵 𝑌 2 . 9 c m , 𝐶 𝑍 6 . 1 c m

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.