Draw a regular pentagon on a base AB 35mm long, within it inscribe the largest equilateral triangle.
To draw a regular pentagon with an inscribed equilateral triangle, follow these steps:
1. Start by drawing a line segment AB of length 35mm. This will be the base of the pentagon.
2. To construct a regular pentagon, we need to divide the base AB into five equal segments. Measure 35mm and mark points C and D on the line AB such that AC = CD = DB = 35mm/5 = 7mm.
3. From point C, draw a line segment CE perpendicular to AB. Measure 35mm on the compass and draw an arc from point E intersecting the line AB at point F.
4. From point D, draw a line segment DF perpendicular to AB. Measure 35mm on the compass and draw an arc from point F intersecting line AB at point G.
5. From point G, draw a line segment GH perpendicular to AB. Measure 35mm on the compass and draw an arc from point H intersecting line AB at point I.
6. From point I, draw a line segment IJ perpendicular to AB. Measure 35mm on the compass and draw an arc from point J intersecting line AB at point K.
7. Connect the points from A to K, K to E, E to G, G to I, and I to C. This will complete the regular pentagon ABCDE.
8. To inscribe the equilateral triangle, connect the midpoints of the sides of the pentagon. From points A, B, C, D, and E, draw lines connecting them to form the inner equilateral triangle.
Remember to use a ruler and a compass to ensure accurate measurements and straight lines.