- SQUR is a square.
m^6 XU R= 3 x−9, andSU=x
Find the length of both diagonals.
(Hint: Draw and label a picture. Remember the name of a polygon lists the vertices in a circular order.)
Answer:
3 x− 9 = 45 SU=QR= 18
x= 18Information Overload –Quite a few theorems are presented in this chapter. Remembering them all and which
quadrilaterals they apply to can be a challenge for students. If they are unsure, and cannot check reference material,
a test case can be drawn. For example: Do the diagonals of a parallelogram bisect the interior angles of that
parallelogram? First they need to draw a parallelogram that clearly does not fit into any subcategory. It should be
long and skinny, so no rhombi properties are mistakenly attributed to it. It should also be well slanted over, so as
not to be mistaken for a rectangle. Now they can draw in the diagonals. It will be obvious that the diagonals are not
bisecting the interior angles. They could also try to recreate the proof, but that will probably be more time consuming
and it requires a bit of skill.
Additional Exercises:
- DAVE is a rhombus with diagonals that intersect at pointX.
DX=3 cm, andAX=4 cm
How long is each side of the rhombus?
Answer:
32 + 42 =DA^2 since 4 DX Ais right
DA= 5
DA=AV=V E=ED=5 cmTrapezoids
Average for the Median –Students who have trouble memorizing formulas may be intimidated by the formula for
the length of the median of a trapezoid. Inform them that they already know this formula; it is just the average. The
application of the formula makes since, the location of the median is directly between the two bases, and the length
of the median is exactly between the lengths of the bases. They will have no problem finding values involving the
median.
Where Are We? –Most students have five other classes and a demanding social and family life. It is easy for
them to forget how what they are learning today relates to the chapter and to the class. Use the Venn diagram of the
classification of quadrilaterals to orient them in the chapter. They are no longer learning about parallelograms, but
have moved over to the separate trapezoid area. When student are able to organize their new knowledge, they are
better able to retain and apply it.
Does it Have to be Isosceles? –Students may have trouble remembering which theorems in this section apply only
to isosceles trapezoids. Note that base angle, and diagonal congruence apply only to isosceles trapezoids, but the
relationship of the length of the median to the bases is the same for all trapezoids.
Chapter 2. Geometry TE - Common Errors