Parallel or Congruent –When looking at a marked figure students will sometimes see the arrows that designate
parallel segments and take that the segments to be congruent. This could be due to the misreading of the marks, or
mistakenly thinking parallel always implies congruence. Warn students not to make this error. The last method of
proof in this section which utilizes that one pair of sides are both congruent and parallel, along with an example of
a trapezoid where the parallel sides are not congruent, will help students remember the difference.
Additional Exercises:
- KATE is a parallelogram with a perimeter of 40 cm.
KA= 3 x+8, andAT=x+ 4
Find the length of each side.
(Hint: Draw and label a picture. Remember the name of a polygon lists the vertices in a circular order.)
Answer:
2 ( 3 x+ 8 )+ 2 (x+ 4 ) = 40 KA=ET=14 cm
x= 2 AT=KE=6 cm- SAMY is a parallelogram with diagonals intersecting at pointX.
SX=x+5,X M= 2 x− 7 ,AX= 12 x
Find the length of each diagonal.
Answer:
x+ 5 = 2 x− 7 SM=34 cm
x= 12 AY=288 cm- JEDI is a parallelogram.
m^6 J= 2 x+60, andm^6 D= 3 x+ 45
Find the measures of the four angles of the parallelogram.
Does this parallelogram have a more specific categorization?
Answer:
2 x+ 60 = 3 x+ 45 All four angles measure 90 degrees.
x= 15 JEDI is a rectangle.Rhombi, Rectangles, and Squares
The Power of the Square –Students should know by the classification of quadrilaterals that all the theorems for
parallelograms, rectangles, and rhombi, also apply to squares. It is a good idea to talk about this in class though in
case they have not put it together on their own. A combination of these theorems and the definition of a square can
be combined to from some interesting exercises.
Key Exercises:
2.6. Quadrilaterals