Geo 9 Ch 5 1 5.1 Quadrilaterals Parallelograms/Real World Visual ...

Geo 9 Ch 5 20SUPPLEMENTARY PROBLEMS CH 5 QUADRILATERALS1. Given that P = (-1,-1), Q = (4,3), A = (1,2) and B = (6,k), find the value of k that makes the line AB.(a) parallel to line PQ ;(b) perpendicular to line PQ.2. Let A = (-6,-4), B = (1,-1), C = (0,-4), and D= (-7,-7).a) Show that the opposite sides of the quadrilateral ABCD are parallel. Such a quadrilateral is called aparallelogram .b) Find the lengths of all the sides. What is your conclusion?c) Find the point of intersection of AC and BD (called the diagonals of the parallelogram ) and call itM. Find AM and MC. What can you conclude?3. How can one tell whether a given quadrilateral is a parallelogram? Do the converses of theparallelogram theorems work? Are there any other ways? You might want to draw in an auxiliary lineto help you.4. Given the points A = (0,0), B = (7,1), and D = (3,4), find coordinates for the point C that makesquadrilateral ABCD a parallelogram. What if the question requested ABDC instead?5. The point on a segment AB that is equidistant from A and B is called the midpoint of AB.For each of the following, find the coordinates for the midpoint of AB.(a) A = (-1,5) and B = ( 5, -7)(b) A = (m,n) and B = ( k,l)6. The midsegment of a triangle is a segment that connects the midpoints of 2 sides of the triangle. Givena triangle with coordinates A (1, 7) , B (5,3) and C (-1, 1) find the segment that connects that midpointsof sides AB and AC, label the midpoints M and N, respectively.(a) Find the length of the midsegment MN and compare it to the length of BC.(b) What can be said about the lines containing segments BC and MN?7. Find the point of intersection of these two lines2x + 3y = 6 and x – 4y = 2.8. An equilateral parallelogram is called a rhombus. A square isa simple example of a rhombus. Show that the lines3x – 4y = -8, x = 0, 3x – 4y = 12, and x = 4 form thesides of a rhombus. Support your answer.