Warm-up for 2.4 Deductive Reasoning Handshake problem. If there are two people, there is one handshake between them. If there are three people there are three handshakes. Fill in the table below and then try to find the formula. Hint: Draw points for people. A line between them is a handshake. This is one method to solve the problem. Number of people 1 2 3 4 5 6 … n Number of handshakes

H.W. Answers to pg 99-100 #3-15 odd and #22 pg 105-106 #1-6 all#s 3. 10,000, 100,000. Each term is 10 times the previous 5. 17, 21. Four is subtracted from each term to get 7. 21, 34. To find each term, you add the two previous terms. 9. 10, 24. To get from term to term, you subtract 2, then subtract 4, then subtract 6, and so on. 11. Each figure has one more point than the previous figure. Each point in a figure is connected to each of the other points.

H.W. Answers continued… 13. To get the next figure, add one row to the bottom and one column to the right of the previous figure, and then shade all the rectangles in the bottom row but the rightmost one. 22. 7th term: 56; 10th term: 110; 25th term: 650. In each figure, the number of columns of dots is one greater than the number of rows..

Number of triangles: 1 2 3 4 n -2 33 5. 8n; 1600 H.W. Answers continued… 1. 6n – 3 For 20; f(20) = 6(20) – 3 = 117 2. -3n + 4 For 20; f(20) = -3(20) + 4 = -56 3. 8n – 12 For 20; f(20) = 8(20) – 12 = 148 4. 33 Number of sides: 3 4 5 6 n 35 Number of triangles: 1 2 3 4 n -2 33 5. 8n; 1600 Figure number : 1 2 3 4 5 6 n 200 Number of tiles: 8 16 24 32 40 48 8n 1600 6. 4n – 3 ; for the 200th term it would be 797

Student of the day! Block 1

Student of the day! Block 3

3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x 2.4 Deductive Reasoning Deductive reasoning is using rules that are already established to solve problems. Typical example: Solving for the variable with Algebra. 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x

Another example of using deductive reasoning Conjecture: If an obtuse angle is bisected , then the newly formed two congruent angles are: ____________.

You need to be able to come up with the next two terms of a patter. Quiz on 2.1 to 2.2 You need to be able to come up with the next two terms of a patter. You need to be able to write a rule explaining the patter. You need to be able to determine if a sequence is linear or not. If the sequence is linear, you should be able to determine the function rule. Any questions?

When you are finished with your quiz… ….flip your quiz over …start on the h.w. pg 117 – 118 #1 – 11. When EVERYONE is finished with the quiz, I will return tests. On your test is your average in highligher. The other number is your test grade. If your average is less than a 70% you need to bring in your test signed next class.

Common mistakes on the test Part A: 8) A diagonal is a line segment connecting any two vertices of a polygon. False A diagonal is a line segment connecting any two non- consecutive vertices of a polygon. 11) If two lines intersect, then they are parallel. False If the two lines are on the same plane and don’t intersect then they are parallel. Remember skew lines do not intersect as well. Part C: A chord is a line segment with two points on the circle. A chord CAN go through the center. A diameter is a special chord.