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Geometry Opener(s) 3/31 3/31 It’s National Clams on the Half Shell Day, Tater Day, Oranges and Lemons Day, Bunsen Burner Day, National “She’s Funny That Way” Day and Cesar Chavez Day!!! Happy Birthday Rhea Perlman, Al Gore, Christopher Walken, Leo Buscaglia, Evan ‘Twitter’ Williams, Ewan McGregor, Arthur Rubinstein, Herb Alpert, Liz Claiborne, Cesar Chavez, John Fowles, Octavio Paz, Joseph Haydn and Rene Descartes!!! 3/31 What to do today: 1. Do the opener. 2. Work on Cognitive Tutor. 3. Do the exit pass. TODAY’S OPENER Find x so that l || m. The Last Opener Agenda 1. Algebra 2 Placement Test (30?) 2. Opener (5) 3. Individual Work 1: Creation (8) 4. Individual Work 2: Side Measurement (8) 5. Discussion: Conclusions (8) 6. Exit Pass (5) Standard(s) CCSS-M-G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures Essential Question(s) How do I use similarity and congruence to find numerical relationships among triangle parts? Objective(s) Students will be able to (SWBAT) establish the congruence or non-congruence of two geometric figures. SWBAT establish the similarity or non-similarity of two geometric figures. SWBAT find missing angle measures using congruence or similarity. SWBAT find missing side measures using congruence or similarity Find x so that l || m. Exit Pass The Last Exit Pass HOMEWORK Period 1 No Homework Tonight. HOMEWORK Period 6 No Homework Tonight. Extra Credit Period 1 Period 6 Our Properties So Far… Name/# Description 2/11/14 Algebra Geometry Segments Angles Reflexive Property Symmetric Property Transitive Property Addition & Subtraction Properties Multiplication & Division Properties Substitution Property Midpoint Theorem (2.8) Segment Addition Postulate (2.9) Angle Addition Postulate (2.11) Anything equals itself! Switching preserves equality! If the 1st thing = a 2nd, and that 2nd thing = a 3rd, then that 1st thing = the 3rd. If you add or subtract the SAME thing from equal things, then the resulting things are STILL equal. If you multiply or divide the SAME thing from equal things, then the resulting things are STILL equal. If 2 things are equal, then you can replace one with the other in any equation or expression. A midpoint ‘divides’ a segment into 2 = segments. For all #s, x = x. For all #s, if x = y, then y = x. For all #s, if x = y and y = z, then x = z. For all #s, if x = y, then x + z = y + z and x – z = y – z. For all #s, if x = y, then x * z = y * z and x / z = y / z. For all #s, if x = y, then, for example, x + 2 = w is equivalent to y + 2 = w. A point between 2 other collinear points divides a segment into 2 parts of a whole. A point in the interior of 2 angles divides an angle into 2 parts of a whole. Supplement Theorem A linear pair is supplementary. (2.3) Theorem 2.6: s supplementary to the same or to s are . Adjacent s with Complement noncommon sides are Theorem (2.4) complementary. Theorem 2.7: s complementary to the same or to s are . Vertical s are . Vertical Angles Theorem (2.8) Distributive Property If a quantity x is multiplied by a sum of quantities, then that quantity x can be If M is the midpoint of ̅̅̅̅ 𝐴𝐵 , then ̅̅̅̅̅ 𝐴𝑀 ̅̅̅̅̅ 𝑀𝐵. If M is between A and B, ̅̅̅̅̅ + 𝑀𝐵 ̅̅̅̅ . ̅̅̅̅̅ 𝐴𝐵 then 𝐴𝑀 If M is in the interior of DOG, then mDOM + mMOG = mDOG. (The converse is ALSO true!) If A and B form a linear pair, then they are supplementary. If BED and DEN have noncommon sides, then they are complementary. If 1 and 2 are vertical s, then they are . x(a + b) = xa + xb multiplied by each part of the sum. Theorem 2.9: lines intersect to form 4 right s. Theorem 2.10: All right s are . Theorem 2.11: lines form adjacent s. Theorem 2.12: If 2 s are and supplementary, then each is a right . Theorem 2.13: If 2 s form a linear pair, then they are right s. The sum of the measures of Angle Sum Theorem a ’s s is 180°. (4.1) If 2 s of 1 are to 2 s of a 2nd , then their 3rd s are . The m(exterior) of a = Exterior Angle the sum of the m(remote Theorem (4.3) interior 1) and m(remote interior 2). Corollary 4.1: The acute s of a right are complementary. Corollary 4.2: In any , you can’t have more than 1 right or 1 obtuse . If 2 sides of a are Isosceles Triangle congruent, then the 2 base Theorem (4.9) angles of the are congruent. If 2 angles of a are Isosceles Triangle congruent, then the 2 Theorem Converse opposite sides of the are (4.10) congruent. A is equilateral if and only Corollary 4.3 if (iff) it is equiangular. 3rd Angle Theorem (4.2) Corollary 4.4 Each of an equilateral measures 60°. mC + mU + mP = 180°. If C T and U E, then P A. mT = mB + mO. ̅̅̅̅ 𝐹𝑌 ̅̅̅̅, then Angle If 𝐹𝐿 FLY is congruent to Angle FYL. If Angle FLY Angle FYL, ̅̅̅̅ 𝐹𝑌 ̅̅̅̅ then 𝐹𝐿 If C O W, then COW is equilateral. If ̅̅̅̅ ̅̅̅̅̅ 𝐶𝑂 𝑂𝑊 ̅̅̅̅̅ 𝑊𝐶 , then COW is equiangular. The mC = mO = mW = 60°. Notes: Parallel Postulates 1 3-21 2 3 4 5 6 7 CO s || lines Postulate AE s || lines Postulate CI s || lines Postulate AI s || lines Postulate lines || lines Postulate Parallel Postulate 8 If corresponding s are , then lines are ||. If alternate exterior s are , then lines are ||. If consecutive interior s are supplementary, then lines are ||. If alternate interior s are , then lines are ||. If 2 lines are to the same line, then lines are ||. You are given a line and a point not on the line. There is ONLY ONE line through that point that’s || to the given line.