The parallelogram and its tests
Answers are for parents and teachers.
1
The sides of a parallelogram are in the ratio 2 : 3 and the perimeter is 80 cm. How long is the shorter side (cm)?
16
2
One angle of a parallelogram is 40° larger than the adjacent angle. How many degrees is the larger angle?
110
3
The diagonals AC = 16 cm and BD = 22 cm of a parallelogram meet at O and AB = 10 cm. What is the perimeter of triangle AOB (cm)?
29
4
The angles of a quadrilateral in order are 80°, 100°, 80°, 100°. Is it a parallelogram? Say why.
Yes: its opposite angles are equal in pairs (test 4).
5
Explain in your own words why a diagonal cuts a parallelogram into two congruent triangles.
The diagonal is a common side, and the angles next to it are equal as alternate interior angles; by the side-and-two-angles test the triangles are congruent.