QA Review # 1 a)You must be 21 years old to watch a R movie. Jack is 17 years old. Therefore, Jack can’t watch the movie. b)Jacky is taller than Joe. Joe is taller than Amie. Therefore, Jacky is taller than Amie. c)Movie tickets are on sale for groups of 7 or more people. There are 6 people in Juan’s family. They can buy tickets on sale. d)Maria’s palm tree was 10 inches tall last year. This year, it grew to be 11 inches tall. Next year, Maria’s palm tree will be 12 inches tall. Which of the following is an example of inductive reasoning?

I. A number is even if it is divisible by 2. The number 10 is divisible by 2. Therefore, 10 is even. II. Mr. Julian ate 20 eggs on January, 25 eggs on February, and 30 eggs on March. Therefore, Mr. Julian will eat 35 eggs on April. Which statement(s) use(s) deductive reasoning? Inductive reasoning? Why? QA Review # 2

1.Give me an example a real life example of inductive reasoning? 2.Find 1 counterexample to show that each conjecture is false. a.The sum of two integer numbers is always positive. b.The quotient of any two number is less than 1. c.The product of two fraction numbers is always equal to a fraction. d.The difference of any two numbers is always negative. QA Review # 3

1.“A triangle with sides of three different lengths must be a right triangle.” counterexamples. Give me 1 counterexamples. 2. “If rectangle A is parallel to rectangle B, then all the lines in rectangle A are parallel to all of the lines in rectangle B.” 1 counterexamples. Give me 1 counterexamples. 3. Mr. Julian ran 1 mile on Monday, 4 miles on Tuesday, 9 miles on Wednesday. Therefore, Mr. Julian will run 16 miles on Thursday. Is it Inductive reasoning? Why or why not? QA Review # 4

1.“A triangle with sides of three different lengths must be an obtuse triangle.” counterexamples. Give me 1 counterexamples. 2. “If Plane A is parallel to Plane B, then all the lines in Plane A are parallel to all of the lines in Plane B.” 1 counterexamples. Give me 1 counterexamples. 3. For a regular polygon with n sides, the measure of each interior angle is given by the formula: If there is a Polygon with 3 sides what is its interior angle? Hint: A triangle has 3 sides. QA Review # 5

Two parallel lines are cut by a transversal as shown below. Of the two angles shown, what is the measure of the larger angle? 3x +40 2x - 30 QA Review # 6

Look at the figure below. If m< 1 ≠ m< 5, then lines j and k are not parallel to one another. What can you assume about the properties of this figure? 1)m<1 __ m<4? 3) m<5, m<3 2)m<3__ m<6? Supplementary angle? 4) m<5 and m<6 Complementary angles? QA Review # 7

Look at the figure below. B is an obtuse angle. Complementary Angles : 2 angles that have their sum equal to 90. Supplementary Angles: 2 angles that have their sum equal to 180. Assuming that m< A = m< B leads to a contradiction with the given statement, tell me statements that leads to the contradiction? a b c d 1)m<A and m< B are supplementary 2)Since m<A = m<B, then m<A = 90* and m<B = 90* because their sum has to equal 180*. 3)This is impossible since m<B is an Obtuse angle. QA Review # 8

Two parallel lines are cut by a transversal as shown below. If m< A = 75º, what is m< F? a c d b e f h g QA Review # 9

Lines J and K are cut by a transversal as shown below. Given that lines J and K are parallel, What theorem can be used to prove <1≈ <2 ? What theorem can be used to prove <4 ≈<2? What can we say about <5 and <2= ? J K 5 QA Review # 10

What is m< ABC ? m<YXB? m<XBY? A B C X Y QA Review # 11

1) What can you say about m<BAC = ? ; m<BCA = ? 2) What else can you say about m< b and m<A? 50 A B C E D QA Review # 12

1)Prove that two lines intersected by a transversal are parallel. Just write down the Theorem you would use. 2)What is the measure of an exterior angle of a regular pentagon? 3)What is the measure of an exterior angle of a regular hexagon? 4)What is the measure of an exterior angle of a regular octagon? <1 <2 <4 1)Converse of the Alternate Interior Angles Theorem 1)Converse of the Alternate Interior Angles Theorem: If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. 2)Converse of the Same-Side interior angles 2)Converse of the Same-Side interior angles that are supplementary, then the two lines are parallel. 3) Converse Corresponding Angles Postulate: 3) Converse Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent. QA Review # 13 <3

1) What is the value of x? 2) What is the value of x? x x x x 3x 3x x + 30 x + 30 x QA Review # 14

Find the value for x? x +25 QA Review # 15

1)If the measure of each interior angle of a regular polygon is 140º, how many sides does this polygon have? 2)What is the length AB ? A (a,0) B (b, e) C (b, 0) QA Review # 16

What is the measure of x, y, z ? x x z y QA Review # 17

1)If the measure of each interior angle of a regular polygon is 150º, how many sides does this polygon have? 2)What is the length BC ? A (0,0) B (b, e) C (c, 0) QA Review # 18

What is the value of x? y? z? x x x + 5 x – 15 x x x x x x x x y y z QA Review # 19

Given : AB Construct : XY so that XY | AB at the midpoint M of AB. Take out your compass and construct a perpendicular bisector. 1.Put the compass point on point A and draw a long arc as shown. Be sure the opening is greater than ½ AB. 2.With the same compass setting, put the compass point on the point B and draw another long arc. Label the points where the two arcs intersect as X and Y. 3.Draw XY. The point of intersection of AB and XY is M, the midpoint of AB. XY | AB at the midpoint of AB, so XY is the perpendicular bisector of AB. AB QA Review # 20

Given : Line l and point N not on l. Construct : Line m through N with m || l. Take out your compass and construct the line parallel to a given point that is not on the line. 1.Label two points H and J on l. Draw HN. 2.Construct <1 with vertex at N so that <1 ≈ < NHJ and the two angles are corresponding angles. Label the line you just constructed m. 3.m || l. N l QA Review # 21

Bell Work 1) What is the value of x? 2) What is the value of x? x x x 3x x x + 60 x + 30 x

1)If the measure of each interior angle of a regular polygon is 180º, how many sides does this polygon have? 2)What is the length BC ? A (0,0) B (b, e) C (c, 0) Bell Work

1)If the measure of each interior angle of a regular polygon is 135º, how many sides does this polygon have? 2)What is the length AB ? A (x,y) B (b, e) C (c, d) Bell Work

1)A) If the measure of each interior angle of a regular polygon is 120º, how many sides does this polygon have? B) 144º? C)140º? D) 156º? 1)What is the length AB ?BC?AC? A (x,y) B (w, z ) C (u, v) Bell Work

Two parallel lines are cut by a transversal as shown below. Of the two angles shown, what is the measure of the larger angle? 3x +25 2x - 15 Bell Work

Two parallel lines are cut by a transversal as shown below. Of the two angles shown, what is the measure of the larger angle? 2x +45 2x - 15 Bell Work

Look at the figure below. If m< 1 ≠ m< 5, then lines j and k are not parallel to one another. What can you assume about the properties of this figure? 1)m<1 __ m<4? 3) m<5, m<3 2)m<3__ m<6? Supplementary angle? 4) m<5 and m<6 Complementary angles?

1)Prove that two lines intersected by a transversal are parallel? 2)What is the measure of an exterior angle of a regular pentagon? 3)What is the measure of an exterior angle of a regular hexagon? 4)What is the measure of an exterior angle of a regular octagon? <1 <2 <4 1)Converse of the Alternate Interior Angles Theorem 1)Converse of the Alternate Interior Angles Theorem: If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. 2)Converse of the Same-Side interior angles 2)Converse of the Same-Side interior angles that are supplementary, then the two lines are parallel. 3) Corresponding Angles Postulate: 3) Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent.

Look at the figure below. If m< 1 ≠ m< 5, then lines j and k are not parallel to one another. What can you assume about the properties of this figure? Bell Work

Warm Up # 9 Indirect Proof: Assume what you need to prove is false, and then show that something contradictory (absurd) happens. Assume that the opposite of what you are trying to prove is true. From this assumption, see what conclusions can be drawn. These conclusions must be based upon the assumption and the use of valid statements. Search for a conclusion that you know is false because it contradicts given or known information. Oftentimes you will be contradicting a piece of GIVEN information. Since your assumption leads to a false conclusion, the assumption must be false. If the assumption (which is the opposite of what you are trying to prove) is false, then you will know that what you are trying to prove must be true.