constructing triangles using geometer’s sketchpad

Constructing Triangles using Geometer’s Sketchpad

Drawing Triangles

You will need to do this each time you want to construct a triangle:

• Open Geometer’s Sketchpad

Drawing Triangles

You will need to do this each time you want to construct a triangle

Click on the straightedge tool

Drawing Triangles

Click in the window and then hold the mouse, moving it along. The line will

appear. Stop moving the mouse when the line is as long as you want. Then

click on the arrow tool.

Drawing Triangles

• If you need to measure the length of the line segment, first highlight the line and then click “measure length”

Drawing Triangles

• To construct the second side of the triangle, repeat the process for constructing a line segment. Begin the line segment at the end of the first line segment.

Drawing Triangles

• To construct the third side of the triangle, repeat the process for constructing a line segment. Begin the line segment at the end of the second line segment and extend it to the first.

Drawing Triangles

• The perimeter of the triangle can be measured (simply add up the length of the 3 sides)

• The area of the triangle can be measured.

• Click on the three vertices, and choose the “construct menu” – polygon area command.

Drawing Triangles

If a triangle with specific measurements for 3 sides is needed, the process to construct the triangle is different.

• Begin by constructing the first side. Use the “measure length” tool as before.

Drawing Triangles

• Next, adjust the length of the line segment to the desired length.

• This is done by first selecting the “selection arrow tool”

Drawing Triangles

• Then click on one end of the line segment, hold down the mouse and move the point.

• Notice how the length of the line segment changes.

• Stop when the desired length is reached.

Drawing Triangles

• Repeat the previous step and draw the other 2 sides.

• Leave the sides as 3 separate lines for the time being

Drawing Triangles

• Move the longest side so that there is room to construct the triangle

Drawing Triangles

• We don’t know exactly where the other 2 sides go, so we draw small circles to show where the end points of the other 2 sides go.

Drawing Triangles

• Choose the “compass tool”

• Choose one end point of the line and click on it. Move the point away from the line.

Drawing Triangles

• A circle appears

• Then click on the “selection arrow tool”

Drawing Triangles

• Then click anywhere on the circle.

• Using the measure pull-down menu, select “radius” and measure the radius of the circle.

Drawing Triangles

• Then click on any point on the circle, and move the point out or in, so that the radius is the same as one of the lengths of the other 2 lines.

Drawing Triangles

• Repeat the process with the other end of the base line. Click on the end point, choose the “compass” tool and extend the point out until it forms a circle.

Drawing Triangles

• Repeat the measuring of the measuring of the radius. First click on the selection arrow tool, then click on the second circle, and measure its radius. Adjust its size until it matches the length of the 3rd side.

Drawing Triangles

• The points where the circles intersect can be considered for the vertex of the triangle. Click one of these points and one end of the base line.

• Using the construct menu, select “segment” and a side of the triangle appears.

Drawing Triangles

• Repeat the previous steps with the other side of the base line.

• Construct the segment.

Drawing Triangles

• You can choose to hide the circles by first clicking on just the circles, and then using the display menu, choosing the “hide circles” option.

Drawing Circles

• You can also hide point “O” – the centre of the circle, by right clicking on it and then selecting “hide point”.

Drawing Triangles

• To draw a triangle when you know the length of one side and the measurement of 2 angles.

• Begin by constructing the base line, and adjusting it to the desired measurement

Drawing Triangles

• Then construct the 2nd side of the triangle by drawing a second line.

Drawing Triangles

• Then click on the “selection arrow tool” and then click on the 3 points – the ends of the lines and the point where they intersect.

Drawing Triangles

• Then using the measure toolbar, measure the angle that is formed.

Drawing Triangles

• Adjust the newest line so that the angle measure corresponds with the required angle.

Drawing Triangles

• Click on the right end point of the base, and draw a third line

Drawing Triangles

• Once again, click on the three points of this new angle and measure it.

Drawing Triangles

• Adjust the angle so that it corresponds to the required measurement.

Drawing Triangles

• Click on the intersection point of the angles to form the third vertex of the triangle.

Drawing Triangles

• To get rid of extra lines, click on the three vertices of the triangles and then construct the segments.

Drawing Triangles

• Then right click on extraneous points and hide them.

• Right click on extra segments and hide them.