Quadrilaterals
Primary 5 parallelogram angle questions: opposite angles are equal and angles between parallel sides add to 180°, in rhombuses and trapeziums too.
Questions in this lesson
Transcript
A B C D is a parallelogram. Angle B A D is one hundred and sixteen degrees. Find angle A D C. Five four-sided figures each have their own name. Square, rectangle, parallelogram, rhombus and trapezium. The square and the rectangle have a right angle at every corner. That small box is how a figure says 90 degrees. The other three have parallel sides, and the arrowheads show which. Each pair of parallel sides has its own arrowheads. The sum of each pair of angles between 2 parallel sides is one hundred and eighty degrees. Angle B A D and angle A D C are that pair. So angle A D C is one hundred and eighty minus one hundred and sixteen, which is 64 degrees. The bracket underneath says which property gave it. Now angle B C D. You could take one hundred and eighty minus 64 along D C. Or see it at once: it faces angle B A D across the figure, so they are equal. Both ways give one hundred and sixteen degrees. That is opposite angles of a parallelogram.
Your turn. P Q R S is a trapezium with P Q parallel to S R. Angle P S R is one hundred and eight degrees. True or false: angle S P Q is one hundred and eight degrees. Try it first. Pause if you like. P Q and S R are parallel, so the two angles between them add up to one hundred and eighty degrees. Angle S P Q is one hundred and eighty minus one hundred and eight, which is 72 degrees. The bracket names the property. 72 is not one hundred and eight, so the statement is false. The arrowheads say P Q and S R are parallel. One hundred and eight and 72 are the two angles between them. Between a pair of parallel sides, the two angles add up to one hundred and eighty degrees.