Use the properties of quadrilaterals to determine the number of quadrilaterals that can be constructed with congruent opposite sides and supplementary consecutive angles
There are two types of quadrilaterals that can be constructed with congruent opposite sides and supplementary consecutive angles – parallelograms and rhombuses.
1. Parallelograms have opposite sides that are parallel and congruent, and consecutive angles that are supplementary. This means that the opposite sides are equal in length, and the sum of the two adjacent angles adds up to 180 degrees. There are an infinite number of parallelograms that can be constructed with these properties, as long as the opposite sides are equal in length and the consecutive angles add up to 180 degrees.
2. Rhombuses have all four sides equal in length, and opposite angles are equal in measure. If the consecutive angles are supplementary, it means the angles are 90 degrees each. Therefore, a rhombus with congruent opposite sides and supplementary consecutive angles would be a square. So, there is only one quadrilateral that fits these criteria, which is a square.
In conclusion, there are an infinite number of parallelograms that can be constructed with congruent opposite sides and supplementary consecutive angles, and only one quadrilateral, which is a square.
Identify the quadrilaterals that can be constructed with congruent diagonals that bisect each other
Responses
trapezoid and rhombus
square and rectangle
rectangle and parallelogram
rhombus and kite