The 3D graphic below shows a sculpture based on intersecting planes - Leaving Cert DCG - Question A-3 - 2015

In the plan view, draw a straight line connecting points B and D, which represents the line of intersection. In the elevation view, replicate this line accordingly, ensuring that it maintains the correct angles relative to the plane outlines presented for ABC and ADE.

Construct horizontal and vertical auxiliary lines that are parallel to the line of intersection drawn. For instance, project line segments from points A and D in both plan and elevation. This will aid in visualizing the spatial relationship of the planes.

Project the planes ABC and ADE onto the auxiliary view by transferring the significant points using projection lines. This will help depict how these planes would appear in a different dimensional perspective, clarifying their orientation.

Draw perpendicular lines X2 and Y2 from the line of intersection to uphold the correct measure of its true length. These lines should intersect the initial projection lines, defining the accurate dimensions of the intersection.

Create a second auxiliary view that shows the projected representation of the planes ADE and ABC. Use the intersection lines as a reference to visualize and project the planes accurately in this view.

Measure the angle formed between the two planes at the line of intersection. This dihedral angle is pivotal in understanding the spatial relationship between the planes. Use a protractor for precise measurement or apply trigonometric formulas if applicable.

To establish the horizontal trace of the plane ADE, analyze the intersection of the plane with the horizontal plane (typically the XZ or XY plane). This trace will typically be drawn as a line showing where ADE intersects the horizontal reference plane.

For the vertical trace, identify how the plane ADE intersects with the vertical plane (usually the YZ plane). Mark the intersection points accurately on the vertical axis, and connect them to formulate the trace of the plane ADE.