temp.notebook October 27, 2017 Daily Affirmations

Transcription

1 Let's st for our Daily Affirmations Today is a good day! I will LET Go of the past that I do not need CREATE the future that I want. I believe in myself my abilities. I will persist until I succeed. I say positive things about myself to myself. I can learn anything. I can know anything. I can be anything. I find joy in the journey. EO1 Opp #1 Th/F, Sep 7 8 H back ML Wednesday, Sep 13th Due Tue, Sep 19th Math 3 Semester 1 Overview EO1 One Variable Inequalities 12.5% EO2 Two Variable Inequalities 12.5% EO3 Similarity 12.5% EO4 Congruence 12.5% EO5 Quadratic Polynomials 12.5% EO6 Normal Distribution 12.5% S1 Midterm 10% EO2 Opp #1 M/T, Sep H back Friday, Sep 29th Due Thu, Oct 5th ML EO3 Opp #1 M/T, Oct H back Friday, Oct 20th Due Fri, Oct 27th ML EO4 Opp #1 M/T, Nov 6 7 ML H back Monday, Nov 13th Due Thu, Nov 16th EO5 Opp #1 Th/F, Nov 30 Dec 1 H back ML Wednesday, Dec 6th Due Thu, Dec 14th EO6 Opp #1 Th/F, Dec ML S1 Final Level 2 Opp #2 W/Th, Dec EO1 Opp #2 Thu, Sep 21st 6am B113 Huff 2:29 D213 Cox EO2 Opp #2 Tue, Oct 10th EO3 Opp #2 Tue, Oct 31st 6am B113 Huff 6am B113 Huff 2:29 B212 Trantham 2:29 B213 Rozum EO4 Opp #2 Tue, Nov 28th 6am B113 Huff 2:29 B213 Erickson EO5 Opp #2 Mon, Dec 18 in class 6am B113 Huff 2:29 D211 Riley

2 ? Inv 1 p198 #6, STM, CYU, EQ Triangle Centers (finish at home if you don't finish in class) EO4 Quiz #1 Individual Inv 3 p205 #2 Proofs Practice #1 4 Proofs Practice #5 8 Proofs Practice #9 11 Proofs Practice #12 13 Proofs Practice #14 19 Triangle Centers (hout) Due Fri, Oct 27th p204

3 Essential Questions How can congruent triangles establish properties of special quadrilaterals what are those properties? Language Objective Mathematicians will be able to......state the special properties of parallelograms, rectangles, rhombuses with regard to congruence parallel lines. Activities #1 7, STM, CYU, EQ p200 Homework: Finish this investigation!

4 In Activity #1 on your calendar... Kite Quadrilaterals Parallelogram Trapezoid Rectangle Rhombus Square Kite 2 pair of consecutive, congruent Quadrilaterals A closed, four sided polygon Parallelogram Opposite parallel OR Opposite congruent Rhombus 4 congruent Square 4 right angles AND 4 congruent Trapezoid Exactly one pair of parallel Rectangle 4 right angles

5 p205 GIVEN In Activity #2, write your proof for part a. STRATEGY Statement Reason Given Reflexive Prop SSS Thm CPCTC Converse of the Alt Int Ang Thm GIVEN In Activity #3, write your proof for part b. STRATEGY Statement Reason Given Reflexive Prop Alt Int Thm ASA Thm CPCTC

6 Math 3 EO4 TOOLKITS Congruence Congruence Theorems Flip Book Tips for Writing Congruence Proofs Triangle Centers Properties of Quadrilaterals TOOLKIT: Triangle Congruence Flip Book

7 temp.notebook October 27, 2017 TOOLKIT: Triangle Congruence Flip Book TOOLKIT: Triangle Congruence Flip Book

8 TOOLKIT: Tips for Writing Congruence Proofs GIVEN: Could be in list, a sentence, or a diagram. PROVE: Typically three options Triangles are congruent = Corresponding parts (angles or side lengths) are congruent = Lines are parallel STATEMENT 1. Proofs typically begin by stating the given information Pick the reason that fits the proof{ 1. Given REASON The body of the proof must include the 3 congruent parts lead to the congruence theorem that you're using: ASA = Thm SAA = Thm SSS = Thm SAS = Thm HL = Thm Your final statement must be exactly the same as what you're asked to prove in the prompt. If proving that triangles are congruent, then your last statement is a congruence statement ASA = Thm SAA = Thm SSS = Thm SAS = Thm HL = Thm If proving that Prove that corresponding parts are congruent, then your last statement is a congurence statement. or NOTE: You must have shown that the triangles are congruent first, then you can use this reason! CPCTC (Corresponding Parts of Congruent Triangles are Congruent) If proving that lines are parallel, then your last statement is a parallel lines statement. If......corresponding angles are congruent......alternate interior angles are congruent......alternate exterior angles are congruent......same side interior angles are supplementary......same side exterior angles are supplementary......then the two lines cut by the transversal are parallel. TOOLKIT: Triangle Centers Circumcenter (perpendicular bisectors) center of a circle circumscribed around the triangle (touches all 3 vertices) equidistant from each vertex (radius of circumscribed circle) on midpoint of hypotenuse: right triangle inside triangle: acute triangle outside triangle: obtuse triangle Incenter (angle bisectors) center of a circle inscribed inside the triangle (touches all 3 ) equidistant from each side (radius of inscribed circle) Centroid (medians) center of gravity (balancing point) centroid cuts every median 2:1 a single median cuts the triangle into two equal areas Orthocenter (altitudes) on vertex: it's a right angle = right triangle inside triangle: acute triangle outside triangle: obtuse triangle

9 TOOLKIT: Kite 2 distinct pairs of consecutive, congruent Properties of Quadrilaterals Parallelogram Opposite are parallel OR Opposites are congruent Rhombus 4 congruent Square 4 right angles AND 4 congruent Trapezoid Exactly one pair of parallel Rectangle 4 right angles

10 Attachments M3 211 Organizer.docx M3 311 Parallel Lines & Transversal Foldable.pdf SelectorTools.exe