Year 9 Interactive Maths - Second Edition

Geometric Constructions

Constructing Triangles

Given Two Angles and a Side

Example 29

Solution:

Step 2

Step 3

Given Three Sides

Example 30

Solution:

Step 2

Using a compass, draw an arc with radius 4 cm and with B as the centre.

Step 3

With A as the centre and with radius 5 cm, draw an arc to cut the arc drawn in Step 2 at C.

Step 4

Join AC and BC. 

ABC is the required triangle.

Given Two Sides and an Angle

Example 31

Solution:

Step 2

Step 3

Draw an arc of radius 8 cm with B as the centre to cut AL (extend the arm AL, if needed) at C.

Step 4

Join BC.

ABC is the required triangle.

Ambiguous Case

Sometimes we can construct more than one triangle with the given measurements.

Example 32

Solution:

Step 2

Step 3

Step 4

Key Terms

geometric constructions, constructing a triangle, protractor, compass

Study Another Topic in Chapter 13: Geometry

[ Angle Facts of Geometry ] [ Parallel Lines ] [ Triangles ] [ Deductive Geometry ] [ Quadrilaterals ] [ Congruence ] [ Similar Triangles ] [ Geometric Constructions ] [ Bisector of an Angle ] [ Perpendicular Bisector of a Line Segment ] [ Perpendicular from a Point on to a Line ] [ Perpendicular at a Point on the Line ] [ Problem Solving Unit ] [ Symbols ] [ Index ]