Use the properties of quadrilaterals to determine the number of quadrilaterals that can be constructed with congruent opposite sides and supplementary consecutive angles.(1 point)

Responses

0
0

1
1

6
6

4

1 proof

To prove that only 1 quadrilateral can be constructed with congruent opposite sides and supplementary consecutive angles, we can use the properties of quadrilaterals.

Given that the quadrilateral has congruent opposite sides, let's call the quadrilateral ABCD, where AB = CD and BC = AD.

Since the consecutive angles are supplementary, let's denote the angles at B and C as x and 180 - x, respectively. Similarly, let's denote the angles at A and D as y and 180 - y, respectively.

Since the sum of the interior angles of a quadrilateral is always 360 degrees, we can write the following equation:

x + y + (180 - x) + (180 - y) = 360
x + y + 180 - x + 180 - y = 360
360 = 360

This equation is true, meaning that our choice of angles x and y satisfy the condition of being supplementary consecutive angles.

Based on these properties and conditions, there is only one quadrilateral that can be formed with congruent opposite sides and supplementary consecutive angles.