Two Different Arcs
Visual of two different compass arcs intersecting to form a scalene triangle.
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The intersection of the two arcs guarantees the correct distance from both endpoints.
Learn the procedural steps to construct a triangle when three valid side lengths are known.
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Introduction to the SSS (Side-Side-Side) construction method.
When given three unequal side lengths (like 4 cm, 5 cm, and 6 cm), the first step is to draw one of these lengths as your base.
While any side can act as the base, it is often easiest to start with either the first given length or the longest length. Let's say we draw a horizontal base .
Visual of two different compass arcs intersecting to form a scalene triangle.
The intersection of the two arcs guarantees the correct distance from both endpoints.
Worked example showing the 4 steps to construct a 4, 5, 6 cm triangle.
Problem. Construct a triangle with side lengths of 4 cm, 5 cm, and 6 cm.
Faded steps to construct a triangle of sides 4, 6, and 8 cm.
To construct a triangle with sidelengths 4 cm, 6 cm, and 8 cm, first draw the base. We can choose the longest side as our base, meaning our starting line segment will be cm long. Next, place the compass pointer at the first endpoint and draw an arc of radius cm. Finally, place the pointer at the other endpoint and draw an intersecting arc of radius cm to locate the third vertex.
MCQ testing if the choice of base matters.
When constructing a triangle with sides , , and , which side MUST be used as the base?
Constructing a triangle with sides 1 cm, 5 cm, and 5 cm.
List the provided side lengths.
Show that the sum of the two smaller sides is strictly greater than the longest side.
Choose one side to act as the base (the unequal side is often easiest here).
State the radii for the two arcs you will draw from the endpoints of the base.
Based on the side lengths, what specific type of triangle will this be?