Download 6-1 Classifying Quadrilaterals

6-1 CLASSIFYING QUADRILATERALS (p. 288-293)
There are many special quadrilaterals (four-sided polygons) that we work with in
Geometry.
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel.
Example: Sketch a parallelogram and use appropriate tick marks.
A rhombus is a parallelogram with four congruent sides (it is equilateral).
Example: Sketch a rhombus and use appropriate tick marks.
A rectangle is a parallelogram with four right angles (it is equiangular).
Example: Sketch a rectangle and use appropriate tick marks.
A square is a parallelogram with four congruent sides and four right angles (it is regular).
Example: Sketch a square and use appropriate tick marks.
A kite is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides
congruent.
Example: Sketch a kite and use appropriate tick marks.
A trapezoid is a quadrilateral with exactly one pair of parallel sides (the bases are
parallel).
Example: Sketch a trapezoid and use appropriate tick marks.
An isosceles trapezoid is a trapezoid whose nonparallel sides (the legs) are congruent.
Example: Sketch an isosceles trapezoid and use appropriate tick marks.
Example: The slope of AB equals the slope of DC. What kind of quadrilateral is
ABCD?
A
D
B
C
Example: Refer to the classifying diagram on p. 289 to answer the next three questions.
1. Why is a square a rhombus?
2. Why is a square a rectangle?
3. Why is a trapezoid not a parallelogram?
Example: Determine the most precise name for the quadrilateral with vertices Q (-4, 4),
B (-2, 9), H (8, 9), and A (10, 4). Use both the slope formula and the distance formula in
your work. Sketching the figure on graph paper is optional.
If time, do 2 on p. 289.
There is plenty of good algebra problems associated with quadrilaterals.
Example: In parallelogram JKLM, m L  2x - 10 and
m
K  3x  50. Set up an
equation and solve for x. Find the measures of the four angles of the parallelogram.
Do 3 on p. 290.
Homework p. 290-293: 3,7,10,11,14,16,20,23,25,29,31,35-37,41,49,60-62,67,70,73
14. kite
16. rectangle
31. Not possible. If a trapezoid has one right angle, then it has a second right angle.
49. rhombus, square, kite, some trapezoids