To construct a triangle when you are given the lengths of all three sides (Side-Side-Side or SSS), you need to use a ruler and a compass. Before drawing, it is important to check if the triangle is possible by using the
Triangle Inequality Theorem. This rule says that the sum of any two sides must be greater than the third side.
Here is the step-by-step method to draw any of these triangles:
1.
Draw the Base: Use a ruler to draw the longest side first. Let's call this the base. Mark the two ends clearly.
2.
Set the Compass for Side 2: Open your compass to the length of the second side. Place the point of the compass on one end of the base and draw an arc above the line.
3.
Set the Compass for Side 3: Open your compass to the length of the third side. Place the point of the compass on the *other* end of the base and draw another arc so that it crosses the first arc.
4.
Connect the Points: The place where the two arcs cross is the top corner (vertex) of your triangle. Use your ruler to draw straight lines from this crossing point down to both ends of the base.
Checking the Triangles in the Worksheet:
All the triangles listed in problems 1 through 8 satisfy the triangle inequality rule (the two shorter sides add up to more than the longest side), so they can all be drawn accurately.
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Problem 1: Draw a 9 cm base. Arcs of 7 cm and 5 cm will meet at the top.
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Problem 2: This is an equilateral triangle. Draw a 2.5 cm base. Both arcs will also be 2.5 cm.
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Problem 3: Draw an 8 cm base. Arcs of 4 cm and 7.5 cm will meet.
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Problem 4: Draw a 6.2 cm base. Arcs of 3.8 cm and 4.2 cm will meet.
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Problem 5: Draw a 7.2 cm base. Arcs of 1.7 cm and 8.2 cm will meet.
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Problem 6: Another equilateral triangle. Draw a 6.6 cm base. Both arcs will be 6.6 cm.
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Problem 7: Draw an 8.4 cm base. Arcs of 9.2 cm and 3.5 cm will meet.
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Problem 8: Draw a 5.2 cm base. Arcs of 3.7 cm and 3.9 cm will meet.
Final Answer:
The task requires constructing 8 specific triangles using a ruler and compass based on the Side-Side-Side (SSS) method. For each problem, draw the longest side as the base, then use a compass to draw intersecting arcs from the endpoints corresponding to the other two side lengths. Connect the intersection point to the base endpoints to complete the triangle. All provided sets of side lengths form valid triangles.
Parent Tip: Review the logic above to help your child master the concept of basic constructions geometry worksheet.
