Question

use the problem from the previous page to help you understand when conditions result in one, more than one, or no quadrilateral. 1 look at the quadrilaterals in the first solve it. how are they different from each other? 2 look at the quadrilaterals in the solve its. why are they not the only quadrilaterals with sides that are 3 cm and 5 cm long? 3 explain why there is only one unique rectangle with side lengths of 3 and 5 but more than one unique parallelogram with side lengths of 3 and 5. 4 when you know all the side lengths of a triangle, there is only one possible triangle you can make. when you know all the side lengths of a quadrilateral, there is more than one possible quadrilateral you can make. why? 5 reflect think about all the models and strategies you have discussed today. describe how one of them helped you better understand how to solve the try it problem.

Explanation:

1. Quadrilaterals can differ in side - lengths, angles, and shapes. For example, a square has all equal sides and right angles, while a trapezoid has only one pair of parallel sides.
2. Given two side - lengths of 3 cm and 5 cm, the angles between the sides can vary, creating different quadrilaterals. The shape is not fixed just by two side - lengths.
3. A rectangle has all angles equal to 90 degrees. So, with side - lengths of 3 and 5, the shape is fixed. In a parallelogram, the angles can vary while keeping the side - lengths 3 and 5, resulting in multiple possible parallelograms.
4. A triangle is rigid because of the SSS (Side - Side - Side) congruence criterion. In a quadrilateral, the angles can change even when all side - lengths are known, allowing for multiple non - congruent quadrilaterals.
5. For example, using a physical model of a quadrilateral made of sticks connected by hinges can help visualize how the shape can change while keeping the side - lengths the same.

Answer:

1. They can differ in side - lengths, angles, and overall shape.
2. Because the angles between the 3 - cm and 5 - cm sides can vary.
3. A rectangle has fixed 90 - degree angles, while a parallelogram's angles can vary.
4. Triangles are rigid due to SSS, and quadrilaterals are not because their angles can change with fixed side - lengths.
5. A physical model of a quadrilateral helped by showing how it can change shape with fixed side - lengths.