Worksheet: Geometric Constructions: Triangles

In this worksheet, we will practice constructing a triangle given its three sides and using its properties to solve problems.

Q1:

Draw a triangle 𝐴𝐵𝐶 in which 𝐴𝐵=3cm, 𝐵𝐶=4cm, and 𝐴𝐶=5cm. Bisect 𝐵 with a line that intersects 𝐴𝐶 at the point 𝐷. Measure the length of 𝐵𝐷.

Q2:

Draw a triangle 𝐴𝐵𝐶 in which 𝐴𝐵=𝐴𝐶=12cm and 𝐵𝐶=15cm. First, bisect 𝐴𝐵 at 𝐷 and 𝐴𝐶 at 𝐸, then connect the points to draw 𝐷𝐸. Using the drawing, determine the length of 𝐷𝐸

Q3:

Draw the triangle 𝐴𝐵𝐶, where 𝐴𝐵=6.2cm, 𝐵𝐶=12cm, and 𝐴𝐶=13cm. Then draw a perpendicular line from 𝐴 to 𝐵𝐶 intersecting it at 𝑋, and a perpendicular line from 𝐵 to 𝐴𝐶 intersecting it at 𝑌. Use the ruler to find the lengths of 𝐴𝑋 and 𝐵𝑌.

  • A𝐴𝑋6.2cm, 𝐵𝑌5.7cm
  • B𝐴𝑋5.7cm, 𝐵𝑌5.7cm
  • C𝐴𝑋6.2cm, 𝐵𝑌5.2cm
  • D𝐴𝑋5.7cm, 𝐵𝑌5.2cm

Q4:

Draw a triangle 𝐴𝐵𝐶, in which 𝐴𝐵=8cm, 𝐵𝐶=6cm, and 𝑚𝐵=120. Then draw a perpendicular line from 𝐴 to 𝐵𝐶 that intersects it at 𝑋, draw another perpendicular line from 𝐵 to 𝐴𝐶 that intersects it at 𝑌, and finally draw a perpendicular line from 𝐶 to 𝐴𝐵 that intersects it at 𝑍. Use the ruler to find the lengths of 𝐴𝑋, 𝐵𝑌, and 𝐶𝑍.

  • A𝐴𝑋6.4cm, 𝐵𝑌3.4cm, 𝐶𝑍4.7cm
  • B𝐴𝑋6.9cm, 𝐵𝑌2.9cm, 𝐶𝑍4.7cm
  • C𝐴𝑋6.4cm, 𝐵𝑌2.9cm, 𝐶𝑍5.2cm
  • D𝐴𝑋6.9cm, 𝐵𝑌3.4cm, 𝐶𝑍5.2cm

Q5:

Draw a triangle 𝐴𝐵𝐶 in which 𝐵𝐶=4cm, 𝐴𝐶=3cm, and 𝑚𝐶=90. Measure the length of 𝐴𝐵.

Q6:

Draw the following triangle accurately, and then draw 𝐵𝐷 so that it bisects 𝐴𝐶 at point 𝐷. Measure the length of 𝐵𝐷.

  • A𝐵𝐷7.8 cm
  • B𝐵𝐷8.7 cm
  • C𝐵𝐷10.8 cm
  • D𝐵𝐷11.4 cm
  • E𝐵𝐷11.9 cm

Q7:

Draw a triangle 𝐴𝐵𝐶 in which 𝐴𝐵=3cm, 𝐵𝐶=4cm, and 𝐴𝐶=4cm. Draw a line 𝐴𝐷, where the line bisects 𝐵𝐶 at point 𝐷. Measure the length of 𝐴𝐷.

  • A𝐴𝐷3.2cm
  • B𝐴𝐷3.7cm
  • C𝐴𝐷2.5cm
  • D𝐴𝐷3.5cm
  • E𝐴𝐷2.9cm

Q8:

Draw the following triangle accurately. Then, measure the length of 𝐴𝐶.

  • A𝐴𝐶10.5cm
  • B𝐴𝐶11.4cm
  • C𝐴𝐶14.6cm
  • D𝐴𝐶14.2cm
  • E𝐴𝐶13.2cm

Q9:

Draw the following triangle accurately. Measure the length of 𝐵𝐶.

  • A𝐵𝐶8.3 cm
  • B𝐵𝐶10.2 cm
  • C𝐵𝐶11.4 cm
  • D𝐵𝐶9.7 cm
  • E𝐵𝐶9.2 cm

Q10:

Draw the following triangle accurately. Draw a line 𝐴𝐷 perpendicular to 𝐵𝐶 and intersecting 𝐵𝐶 at point 𝐷. Measure the length of 𝐴𝐷.

  • A𝐴𝐷5.3cm
  • B𝐴𝐷2.9cm
  • C𝐴𝐷6.1cm
  • D𝐴𝐷5.8cm
  • E𝐴𝐷3.9cm

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