Download 3.2 to 3.4 Classwork Booklet

3.2 Verifying Properties of Triangles
Eg 1) A triangle has vertices O(0, 0), P(8, -4) and Q(4, 4).
a) Find the equation of the median from Q.
b) Find the equation of the right bisector of PQ.
c) Find the equation of the altitude to side OP.
d) The _____________ of a triangle is the point of intersection of the three medians.
Find the centroid of triangle OPQ.
STEP 1
Find the equations of the 3 medians
STEP 2
Intersect any 2 of the medians.
STEP 3
Check that your intersection point lies on the third median.
Formula to find the centroid:
Day 1: Page 124 #1, 3, 4, 6
Day 2: Page 125 #7, 9, 12, 13 (for 12a find the centroid which is (4, 4))
3.4 Verifying Properties of Quadrilaterals – Day 1
Trapezoid = A quadrilateral with _____ pair of parallel sides.
(use ________ __to verify that you have a pair parallel sides)
Rhombus = A quadrilateral in which the lengths of all _______ sides are equal.
(use the __________ formula to verify this)
Note: A square is a special rhombus that has 4 right angles. To prove a quadrilateral is a square
first show it is a rhombus (show all lengths are the same) then find the slope of the 4 sides and
show they are perpendicular.
Kite = A quadrilateral with ______ pairs of ____________ sides equal.
(use _____________ to verify this)
Rectangle = A quadrilateral with ______ pairs of _______ opposite sides and _______ right angles.
(must calculate all 4 lengths and all 4 slopes to verify this)
Parallelogram = A quadrilateral with _______ pairs of __________ sides that are parallel.
(find all 4 slopes to verify this)
Q) For 4b) how do you verify that the diagonals bisect each other?
Q) For #5) a property of quadrilaterals is illustrated– when the midpoints of each side are joined a
parallelogram if formed. Try it with your own picture.
Complete Page 142 #1-5, 7
3.4 Verifying Properties of Quadrilaterals – Day 2
Complete Page 142 #9-12, 14
Recall that to prove two line segments bisect each other, we find the
__________ of each line segment and they must be the ________
point.
To verify that a line segment right bisects another line segment we
must also show that the two line segments intersect at a _______ angle
(verify that the two slope are __________ ________ of one another) in
addition to showing they have the same midpoint).