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Chapter 10: Q5. (page 382)

Describe how you would construct each of the following:

The altitude of 螖ABC that contain vertexA.

Short Answer

Expert verified

The construction of altitude of 螖ABC is described.

Step by step solution

01

Step 1. Given information.   

The given statement is 鈥淭he altitude of 螖ABCthat contains vertexA鈥�.

02

Step 2. Concept used.

An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

03

Step 3. Solution.

The procedure to construct altitude of螖ABC:

  • Consider the line segment BC炉and extend it.
  • Using Aas centre draw two arcs of same radii that intersects the line BC炉at two

Points X鈥�鈥�&Y.

  • With X鈥�鈥�&Yas centers and suitable radius draw two arcs that intersect at point Z.
  • Draw the lineAZ炉.
  • The altitude isAM炉

The construction is shown below:

Therefore, construction of altitude of 螖ABC is described.

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Most popular questions from this chapter

These exploratory exercises can be done using a computer with a program that draws and measures geometric figures.

2. a. Draw any acute 鈻�ABC.Draw the perpendicular bisector of each side of the triangle. They should intersect in one point. Measure the distance from this point of intersection to each of the vertices of the triangle. What do you notice?

b. repeat using an obtuse triangle and a right triangle. Is the same result true for these triangles as well?

c. In a right triangle, the perpendicular bisectors of the sides intersect in what point?

Draw three noncollinear points R,S,and T. Construct a triangle whose sides have R,S,and T as midpoints.

Describe how you would construct each of the following:

The median of 螖ABC that contains vertex B.

Draw any obtuse 螖OBT. Use the SSS method to construct a triangle congruent to 螖OBT.

Repeat Exercise 7, but use the SAS method.
See all solutions

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