10. Copy and complete the table below. Justify your answers by stating the theorem, axiom or corollary used in each case.
Statement (i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rhombus are equal. (iii) Every rectangle is a square. (iv) Every square is a parallelogram. (v)
Every square is a rhombus.
(vi) Every rectangle is a parallelogram. (vii) Every parallelogram is a rectangle. (viii) Every rhombus is a parallelogram.
11. Shown on the right is a diagram used as part of the proof for the theorem which states: In a parallelogram, opposite sides are equal and opposite angles are equal.
Look at triangle 1, ∆ ABD and triangle 2, ∆ BCD . Indicate the sides and angles that can be used to show triangle 1 and triangle 2 are congruent.
23.4 Parallelograms: diagonals bisecting
Discuss and discover
Investigate the diagonals in a parallelogram. (i) Working with a classmate, discuss what you already know about parallelograms.
(ii) Draw a parallelogram. (iii) Using a ruler, draw two diagonal lines as shown in red above.
(iv) Measure the length of one diagonal from one corner to where it crosses the other diagonal. Then measure the length on the same diagonal from the centre to the other corner.
(v) What do you notice about the length from the point where the diagonals cross to the corners on each diagonal?
(vi) Repeat this investigation by drawing two more parallelograms with diagonals drawn on them. (vii) What have you learned about the diagonals of a parallelogram from this task?
B A 1 2 C D True/False Justify
By the end of this section you should understand:
● that the diagonals of a parallelogram bisect one another