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Worksheet: Geometric Constructions

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:

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

Q3:

Draw a triangle 𝐴 𝐡 𝐢 in which 𝐴 𝐡 = 3 c m , 𝐡 𝐢 = 4 c m , and 𝐴 𝐢 = 5 c m . Bisect ∠ 𝐡 with a line that intersects 𝐴 𝐢 at the point 𝐷 . Measure the length of 𝐡 𝐷 .

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

Q4:

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

  • A 𝐴 𝐡 > 𝐴 𝐢
  • B 𝐴 𝐡 < 𝐴 𝐢
  • C 𝐴 𝐡 = 𝐴 𝐢

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

Draw the triangle 𝐴 𝐡 𝐢 , where 𝐴 𝐡 = 6 . 2 c m , 𝐡 𝐢 = 1 2 c m , and 𝐴 𝐢 = 1 3 c m . Then draw a perpendicular line from 𝐴 to 𝐡 𝐢 intersecting it at 𝑋 , and a perpendicular line from 𝐡 to 𝐴 𝐢 intersecting it at π‘Œ . Use the ruler to find the lengths of 𝐴 𝑋 and 𝐡 π‘Œ .

  • A 𝐴 𝑋 β‰ˆ 5 . 7 c m , 𝐡 π‘Œ β‰ˆ 5 . 7 c m
  • B 𝐴 𝑋 β‰ˆ 6 . 2 c m , 𝐡 π‘Œ β‰ˆ 5 . 2 c m
  • C 𝐴 𝑋 β‰ˆ 5 . 7 c m , 𝐡 π‘Œ β‰ˆ 5 . 2 c m
  • D 𝐴 𝑋 β‰ˆ 6 . 2 c m , 𝐡 π‘Œ β‰ˆ 5 . 7 c m

Q11:

Draw the triangle 𝐴 𝐡 𝐢 , where 𝐴 𝐡 = 5 . 8 c m , 𝐡 𝐢 = 1 5 c m , and 𝐴 𝐢 = 1 6 c m . Then draw a perpendicular line from 𝐴 to 𝐡 𝐢 intersecting it at 𝑋 , and a perpendicular line from 𝐡 to 𝐴 𝐢 intersecting it at π‘Œ . Use the ruler to find the lengths of 𝐴 𝑋 and 𝐡 π‘Œ .

  • A 𝐴 𝑋 β‰ˆ 5 . 3 c m , 𝐡 π‘Œ β‰ˆ 5 . 4 c m
  • B 𝐴 𝑋 β‰ˆ 5 . 8 c m , 𝐡 π‘Œ β‰ˆ 4 . 9 c m
  • C 𝐴 𝑋 β‰ˆ 5 . 3 c m , 𝐡 π‘Œ β‰ˆ 4 . 9 c m
  • D 𝐴 𝑋 β‰ˆ 5 . 8 c m , 𝐡 π‘Œ β‰ˆ 5 . 4 c m

Q12:

Draw a triangle 𝐴 𝐡 𝐢 , in which 𝐴 𝐡 = 8 c m , 𝐡 𝐢 = 6 c m , and π‘š ∠ 𝐡 = 1 2 0 ∘ . Then draw a perpendicular line from 𝐴 to βƒ–     βƒ— 𝐡 𝐢 that intersects it at 𝑋 , draw another perpendicular line from 𝐡 to βƒ–     βƒ— 𝐴 𝐢 that intersects it at π‘Œ , and finally draw a perpendicular line from 𝐢 to βƒ–     βƒ— 𝐴 𝐡 that intersects it at 𝑍 . Use the ruler to find the lengths of 𝐴 𝑋 , 𝐡 π‘Œ , and 𝐢 𝑍 .

  • A 𝐴 𝑋 β‰ˆ 6 . 4 c m , 𝐡 π‘Œ β‰ˆ 3 . 4 c m , 𝐢 𝑍 β‰ˆ 4 . 7 c m
  • B 𝐴 𝑋 β‰ˆ 6 . 9 c m , 𝐡 π‘Œ β‰ˆ 2 . 9 c m , 𝐢 𝑍 β‰ˆ 4 . 7 c m
  • C 𝐴 𝑋 β‰ˆ 6 . 4 c m , 𝐡 π‘Œ β‰ˆ 2 . 9 c m , 𝐢 𝑍 β‰ˆ 5 . 2 c m
  • D 𝐴 𝑋 β‰ˆ 6 . 9 c m , 𝐡 π‘Œ β‰ˆ 3 . 4 c m , 𝐢 𝑍 β‰ˆ 5 . 2 c m

Q13:

Draw a triangle 𝐴 𝐡 𝐢 , in which 𝐴 𝐡 = 5 c m , 𝐡 𝐢 = 7 c m , and π‘š ∠ 𝐡 = 1 2 0 ∘ . Then draw a perpendicular line from 𝐴 to βƒ–     βƒ— 𝐡 𝐢 that intersects it at 𝑋 , draw another perpendicular line from 𝐡 to βƒ–     βƒ— 𝐴 𝐢 that intersects it at π‘Œ , and finally draw a perpendicular line from 𝐢 to βƒ–     βƒ— 𝐴 𝐡 that intersects it at 𝑍 . Use the ruler to find the lengths of 𝐴 𝑋 , 𝐡 π‘Œ , and 𝐢 𝑍 .

  • A 𝐴 𝑋 β‰ˆ 3 . 8 c m , 𝐡 π‘Œ β‰ˆ 2 . 9 c m , 𝐢 𝑍 β‰ˆ 5 . 6 c m
  • B 𝐴 𝑋 β‰ˆ 4 . 3 c m , 𝐡 π‘Œ β‰ˆ 2 . 4 c m , 𝐢 𝑍 β‰ˆ 5 . 6 c m
  • C 𝐴 𝑋 β‰ˆ 3 . 8 c m , 𝐡 π‘Œ β‰ˆ 2 . 4 c m , 𝐢 𝑍 β‰ˆ 6 . 1 c m
  • D 𝐴 𝑋 β‰ˆ 4 . 3 c m , 𝐡 π‘Œ β‰ˆ 2 . 9 c m , 𝐢 𝑍 β‰ˆ 6 . 1 c m