Worksheet: Altitudes of Triangles

In this worksheet, we will practice identifying altitudes of a triangle and using their properties to find a missing length.

Q1:

Where is the intersection of the altitudes of this triangle?

  • Aoutside the triangle
  • Bat vertex𝐢
  • Cinside the triangle
  • Dat vertex𝐡

Q2:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐴𝐢?

  • A𝐢𝐷
  • B𝐴𝐹
  • C𝐡𝐸

Q3:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐡𝐢?

  • A𝐢𝐷
  • B𝐴𝐸
  • C𝐡𝐹

Q4:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐴𝐢?

  • A𝐴𝐸
  • B𝐢𝐷
  • C𝐡𝐹

Q5:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐴𝐡?

  • A𝐴𝐹
  • B𝐢𝐷
  • C𝐡𝐸

Q6:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐴𝐡?

  • A𝐢𝐷
  • B𝐡𝐹
  • C𝐴𝐸

Q7:

How many altitudes does this triangle have?

Q8:

Which line segment is the altitude of triangle 𝐴𝐡𝐢 which is perpendicular to ⃖⃗𝐡𝐢?

  • A𝐢𝐷
  • B𝐴𝐹
  • C𝐡𝐸

Q9:

Draw a triangle 𝐴𝐡𝐢 in which 𝐴𝐡=𝐴𝐢=4cm and 𝐡𝐢=5cm. Draw the perpendicular bisectors of each of the three sides. Are the perpendicular bisectors concurrent?

  • Ayes
  • Bno

Q10:

Complete the following statements regarding the position of the intersection point of different triangles’ altitudes.

The concurrency point of an acute triangle’s altitudes lies .

  • Aon one of the triangle’s sides
  • Bon a specific vertex
  • Coutside the triangle
  • Dinside the triangle

The concurrency point of an obtuse triangle’s altitudes lies .

  • Aon the obtuse angle vertex
  • Bon the longest side
  • Cinside the triangle
  • Doutside the triangle

The concurrency point of a right triangle’s altitudes lies .

  • Aon the hypotenuse
  • Boutside the triangle
  • Cinside the triangle
  • Don the right angle vertex

Q11:

True or False: A right triangle has 0 altitudes.

  • ATrue
  • BFalse

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