Name: Period: 6.1 Polygon Sum Polygon: a closed plane figure formed by three or more segments that intersect only at their endpoints. Are these polygons? If so, classify it by the number of sides. 1) 2) 3) 4) 3) Use a straight edge, draw two different quadrilaterals. Carefully measure all the interior angles (if needed, extend the sides), find the sum. How many degrees are in each 4 sided shape? 4) Draw a polygon with 5 sides. Carefully measure all the interior angles (if needed, extend the sides), find the sum. How many degrees are in each 5 sided shape? 5) Fill out the table Number of sides Name of polygon Least number of Interior angle sum 3 Triangle 1 180 0 4 5 6 7 8 9 10 6) Look for a pattern in the completed table, write a general formula for the sum of the angle measures of a polygon in terms of the number of sides, n.
7) Use your conjectures to calculate the measure of each lettered angle 76 0 a = c = 72 0 c b = a b e 38 o d = This is a d e = Regular hexagon f = g = h = i = j = k = m = n = p = q = r = s = t =
Name: 6.2 Exterior Angles of a Polygon 1) What is the name of the polygon to the right? 2) Using the Polygon Sum Conjecture, how many degrees should the interior angles sum to? 3) What should ABC measure? 4) Check your answer using your protractor. 5) Using the Linear Pair Theorem, calculate the measure of one exterior angle at each vertex. Label the diagram. 6) Calculate the sum of the measure of each exterior angle. What is the sum of all exterior angles? 7) What is the sum of the exterior angles, one at each vertex, of the two regular polygons below? 8) a = b = 9. a = b =
10) If the sum of the measures of the interior angles of a polygon equals the sum of the measures of its exterior angles, how many sides does it have? 11) 12) How many sides does a regular polygon have if each exterior angle measures 30? 13) In the space below, construct a quadrilateral which is equiangular but not regular. Use appropriate tools.
Name: Period: 6.3 Trapezoid and kite properties 1. 2. 3. Find the measures of angles 1 and 2 4. Find the measures of angles 1 and 2 5. Find the measures of angles 1 and 2 6. Find the measure of angle 1 7. Find the measure of angle 1 8. What value of n would make PQRS an isosceles trapezoid?
9. 10. What value of x would guarantee EFGH is an isosceles trapezoid 11. A portion of a decorative iron gate has kite shaped portions. The given dimensions are displayed below. a. What is the length of iron bar needed to make 1 of these kite shapes? b. There are 4 kite shapes per cell, how much iron is needed to make 1 cell? One Cell c. If the gate will be 10 feet long, how much iron will be needed to make all of the cells?
Name: Period: 6.4 Security Cameras & Polygons For this activity, assume the security cameras being used can rotate 360 and have an infinite range without losing picture quality. Cameras may be placed on walls or ceilings, but the height of the camera is not a concern because of the range of motion. You have special access to the best equipment that can zoom in on a suspect if needed. Below are seven rooms, as seen from above. Your task is to place the minimum number of security cameras needed in each room, so that all parts of the room can be monitored. For each room, mark where the camera(s) should be placed and write down how many cameras you used.
8. Find a relationship between the number of corners (vertices) in a room and the number of cameras required. You may want to draw rooms with different shapes. 9. Now try to find the minimum number of cameras needed for the museum below, and mark their locations on the floor plan (color pencils may help define the camera s area). According to the rule you found in Question 8, what is the maximum number of cameras the museum would need? Does your floor plan show the same number of cameras or fewer? Why?
13) Measure each side of the trapezoid. Find the midsegment of the trapezoid. Measure the midsegment. How is the midsegment related to the two bases?
Name: period 6.6 Properties of Parallelograms 1) Using the lines on the graph paper, darken a pair of parallel lines at least 6 grids away from each other. Do not make right angles. 2) Using both sides of a straightedge, make a parallelogram. Label the vertices RING 3) Measure each angle R I N G 4) The opposite angles of a parallelogram are 5) Find the sum of the measures of each pair of consecutive angles R + I = N + G = I+ N= G + R = What did you notice? 5) Measure the side lengths in cm RI IN NG GR What did you notice? 6) Finally, on the diagram above, construct the two diagonals RN and IG. Label the point where the diagonals intersect as point H. Measure the length in cm of RH HN and GH IH What did you notice? Given ABCD is a parallelogram, find each of the following 7) Perimeter of ABCD 8) Use properties of parallelograms to find each interior angle measurement, label each angle.
9) 10) 11) 12) 13)
Name: 6.7 Special Parallelograms 1) In the space above, use a double- straight edge (ruler), draw one set of parallel lines. Using the same straight edge, but NOT at right angles to the first set of parallel lines, draw second set of parallel lines that intersect the first pair you drew. a) Compare the lengths of the sides of the parallelogram, what kind of parallelogram did you create? b) With your straight edge, draw in both diagonals. You will need to measure your diagram to make observations about the diagonals. -where do the diagonals intersect each other? -what kind of angles are formed? what do the diagonals appear to do to the angles? -4 smaller Δs are formed, what do you notice about these Δ? Write your observations in sentences: 2) The diagonals of a square are perpendicular bisectors of each other. In the space below, construct a square using only a straight edge and a compass (not a ruler or a protractor) without measuring lengths or right angles. Show all your construction marks. For additional help see: https://www.youtube.com/watch?v=plsty8njytm
3) Using the graph paper as a guide, draw a large rectangle. Draw in both diagonals. Compare the lengths of the diagonals. Write at least two observations about the diagonals of the rectangle: 4) Identify each statement as TRUE or FALSE. If it is false, sketch a COUNTEREXAMPLE or EXPLAIN WHY. a) TRUE or FALSE The diagonals of a rectangle bisect each other b) TRUE or FALSE The diagonals of a parallelogram are congruent c) TRUE or FALSE The diagonals of a rectangle bisect angles. d) TRUE or FALSE Every rhombus is a square e) TRUE or FALSE Every square is a rectangle. f) TRUE or FALSE A diagonal divides a square into two isosceles right triangles g) TRUE or FALSE Opposite angles in a parallelogram are congruent h) TRUE or FALSE Opposite angles in a square are complementary i) TRUE or FALSE The diagonals of a square are perpendicular bisectors of each other. 5) PQRS is a rectangle. OQ = 10. Find PR = 6) ABCD is a parallelogram. If A = 42 0 and DBC = 96 0, find the measure of DBA = 7) KLMN is a square. OM = 2. What kind of triangle is ΔOKL? What kind of triangle is ΔKNM? What is the perimeter of quadrilateral KLMN? In simplified radical form and as a decimal rounded to the nearest hundredth