1. **Problem Statement:** Examine the diagonals of parallelograms by drawing a rectangle ABCD and its diagonals, measuring the diagonals, and exploring their properties. 2. **Step 1: Draw Rectangle ABCD and its Diagonals** - A rectangle is a parallelogram with four right angles. - Draw rectangle ABCD with vertices A, B, C, and D. - Draw diagonals AC and BD. 3. **Step 2: Measure Each Diagonal** - Using a ruler, measure the lengths of diagonals AC and BD. - In a rectangle, the diagonals are equal in length. - So, $AC = BD$. 4. **Step 3: Describe the Property of a Rectangle** - The diagonals of a rectangle are congruent (equal in length). - This is a defining property of rectangles among parallelograms. 5. **Step 4: Explore Diagonals in a Parallelogram That Is Not a Rectangle** - Draw a parallelogram that is not a rectangle (no right angles). - Measure its diagonals. - In general parallelograms, diagonals are not equal. - However, the diagonals bisect each other, meaning each diagonal is divided into two equal parts at the intersection. **Summary:** - In rectangles, diagonals are equal in length. - In general parallelograms, diagonals are not necessarily equal but always bisect each other. This exploration shows the special property of rectangles among parallelograms regarding their diagonals.