Question

Show that quadrilateral abcd is a parallelogram. slope of ab¯¯¯¯¯=4; slope of dc¯¯¯¯¯=4slope of ad¯¯¯¯¯=−1; slope of bc¯¯¯¯¯=−1ab¯¯¯¯¯ is parallel to dc¯¯¯¯¯ because they have the same ¯¯¯¯¯ is parallel to bc¯¯¯¯¯ because they have the same slope.therefore, abcd is a parallelogram. slope of ab¯¯¯¯¯=2; slope of bc¯¯¯¯¯=−12slope of dc¯¯¯¯¯=2; slope of ad¯¯¯¯¯=−12ab¯¯¯¯¯ is parallel to bc¯¯¯¯¯ because (12)(−2)=− ¯¯¯¯¯ is parallel to ad¯¯¯¯¯ because (12)(−2)=−1.therefore, abcd is a parallelogram. slope of ab¯¯¯¯¯=12; slope of dc¯¯¯¯¯=12slope of ad¯¯¯¯¯=−2; slope of bc¯¯¯¯¯=−2ab¯¯¯¯¯ is parallel to dc¯¯¯¯¯ because they have the same ¯¯¯¯¯ is parallel to bc¯¯¯¯¯ because they have the same slope.therefore, abcd is a parallelogram. slope of ab¯¯¯¯¯=2; slope of dc¯¯¯¯¯=2slope of ad¯¯¯¯¯=−12; slope of bc¯¯¯¯¯=−12ab¯¯¯¯¯ is parallel to dc¯¯¯¯¯ because they have the same ¯¯¯¯¯ is parallel to bc¯¯¯¯¯ because they have the same slope.therefore, abcd is a parallelogram.

Answer 1

To show that quadrilateral ABCD is a parallelogram, we can use the slopes of its sides. If opposite sides have the same slope, then they are parallel. The correct option is a.

Step-by-step explanation:

To show that quadrilateral ABCD is a parallelogram, we need to prove that opposite sides are parallel.

Given that the slope of AB is 4 and the slope of DC is 4, we can conclude that AB and DC are parallel because they have the same slope. Similarly, the slope of AD is -1 and the slope of BC is -1, which means AD and BC are also parallel.

Therefore, ABCD is a parallelogram. Hence the answer is a.