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The Triangle is a flat three sided plate defined by the lengths of its three sides. Any triangle can be made – equilateral, isosceles, right angled or scalene – by entering the three side lengths, so it is useful for gussets, stiffeners and triangular infill plates where the side lengths are known but the angles are not. All three corners are sharp.

It appears in the shapes library under Basic Shapes and Triangles.

Insert point and orientation

The insert point is the bottom left corner of the triangle. The Bottom side runs from the insert point along +X to (Bottom, 0). The Left side runs from the insert point up to the top corner, and the Right side runs from the top corner down to the bottom right corner. The top corner is always above the Bottom side (positive Y).

The position of the top corner is worked out from the three lengths:

X = (Left² − Right² + Bottom²) / (2 × Bottom)

Y = √(Left² − X²)

The top corner is not necessarily between the two bottom corners. If Left² is greater than Right² + Bottom² it lies to the right of the bottom right corner (the angle at the bottom right corner is obtuse); if Right² is greater than Left² + Bottom² it lies to the left of the insert point. The default triangle is of the first kind: its top corner is at about X = 81.25, Y = 95.0 mm, to the right of the 50 mm Bottom side.

Properties

Lengths are in the current units (mm or inches). The defaults shown are for a new shape; the inch defaults are used when the program is set to inches.

The dimensions drawn on the shape are Bottom, Left and Right, each along its own side.

Limits

The three lengths must be able to form a triangle: each side must be no longer than the other two added together. If they cannot, the shape is not built and the property page shows Warning: Cannot build shape from these parameters. The same warning appears if Bottom is 0.

•For example, Left 125, Right 50, Bottom 50 cannot be built, because 125 is more than 50 + 50.

•If one side is exactly equal to the other two added together the triangle is flat (zero height): it either builds as a flat sliver or, if rounding makes the height calculation fail, shows the warning above. Either way it has no area.

•Enter positive values. The shape does not check for negative lengths. Left and Right are squared in the calculation, so a negative sign on either has no effect on the shape. A negative Bottom builds the triangle on the other side of the insert point, with the bottom side running along −X.

To make a right angled triangle with the right angle at the insert point, enter the two legs as Left and Bottom and set Right to √(Left² + Bottom²). The Left side is then vertical.

Every 2D shape also has the Transform properties (Base X, Base Y, Rotation, Scale, Mirroring X) and the Polar Array properties, listed after the shape's own properties.