a. Draw a trapezoid with no right

Sure! I can guide you through drawing a **trapezoid with no right angles** step by step. A trapezoid (or trapezium, depending on your region) is a quadrilateral with at least one pair of parallel sides. To ensure there are no right angles in your trapezoid, we'll avoid creating any 90-degree angles during the construction. ### Materials You'll Need: - A piece of paper - A ruler - A protractor (optional, but useful for precise angles) - A pencil ### Step-by-Step Guide: 1. **Draw the First Base:** - Using your ruler, draw a horizontal line segment. This will be the longer base (Base 1) of your trapezoid. For example, draw a line 6 cm long. 2. **Mark the Endpoints:** - Label the left endpoint as point **A** and the right endpoint as point **B**. 3. **Determine the Height and Angles:** - Decide on the desired height (the perpendicular distance between the two bases) of your trapezoid. For instance, let’s choose a height of 4 cm. - Since we want to avoid right angles, we'll draw oblique (non-perpendicular) lines from each endpoint. 4. **Draw the Non-Parallel Sides:** - From point **A**, draw a line segment upward and to the right at, say, a 60-degree angle from the base. Measure 4 cm along this line and mark the endpoint as point **D**. - From point **B**, draw a line segment upward and to the left at, for example, a 120-degree angle from the base. Measure 4 cm along this line and mark the endpoint as point **C**. *(Using a protractor can help you ensure the angles are neither 90 degrees nor parallel to the base.)* 5. **Draw the Second Base:** - Connect points **C** and **D** with a straight line. This will be the shorter base (Base 2) of your trapezoid. - Ensure that Base 2 is parallel to Base 1. Since both sides from **A** and **B** were drawn at angles that are not 90 degrees, the resulting angles at **C** and **D** will also not be right angles. 6. **Finalize Your Trapezoid:** - Trace over your lines to darken the trapezoid's edges. - Label all four vertices (**A**, **B**, **C**, and **D**) if desired. ### Visual Representation: While I can't provide a drawn image here, here's a simple ASCII representation to give you an idea: ``` C ______ D / \ / \ A/____________\B ``` In this diagram: - **AB** and **CD** are the two bases, with **AB** being the longer base. - **AD** and **BC** are the non-parallel sides that are drawn at oblique angles, ensuring there are no right angles in the trapezoid. ### Tips: - **Accuracy:** Using a protractor will help you maintain precise angles and ensure that no angles are 90 degrees. - **Symmetry:** For a symmetrical trapezoid, ensure that both non-parallel sides are angled equally relative to the base. - **Verification:** After drawing, you can check the angles with a protractor to confirm that none are right angles. By following these steps, you'll have a neatly drawn trapezoid without any right angles!