Temp.notebook October 09, Daily Affirmations

Transcription

1 Let's stand for our Daily Affirmations Today is a good day! I will LET Go of the past that I do not need and CREATE the future that I want. I believe in myself and 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 Hand back ML Wednesday, Sep 13th Level 3 Mastery Reform 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 Hand back Friday, Sep 29th Level 3 Mastery Reform Due Thu, Oct 5th ML EO3 Opp #1 M/T, Oct Hand back Friday, Oct 10th Level 3 Mastery Reform Due Thu, Oct 26th ML EO4 Opp #1 M/T, Nove 6 7 Hand back Monday, Nov 13th Level 3 Mastery Reform Due Thu, Nov 16th ML EO5 Opp #1 Th/F, Nov 30 Dec 1 Hand back Wednesday, Dec 6th Level 3 Mastery Reform Due Thu, Dec 14th ML EO6 Opp #1 Th/F, Dec ML S1 Final Level 2 Opp #2 W/Th, Dec EO1 Opp #2 Thu, Sep 21st EO2 Opp #2 Tue, Oct 10th EO3 Opp #2 Tue, Oct 31st EO4 Opp #2 Tue, Nov 28th EO5 Opp #2 Mon, Dec 18 in class

2 ? Inv 312 p172 CYU Proofs Practice 1 Proofs Practice 2 EO3 Quiz Team! EO2 Opp #2 Tue, Oct 10th 6AM B113 Mr. Huff 2:29 B212 Mr. Trantham EO3 Opp #1 M/T, Oct ? EO3 Opp #1 Level 2 & 4 EO3 Opp #1 Level 3 ML

3 p180 No scale factor information available Statement Reason 1. Given 2. Triangle Sum Theorem 3. Addition 4. Subtraction Prop of Equalities 5. Substitution 6. Substitution 7. AA Similarity Theorem No scale factor information available. Statement Reason Given 2. Triangle Sum Theorem 3. Addition 4. Subtraction Prop of Equalities 5. Substitution 6. Triangle Sum Theorem 7. Addition 8. Subtraction Prop of Equalities 9. Substitition 10. AA ~ Thm

4 No scale factor information available. Statement is an isosceles triangle 3. and Reason 1. Given 2. Def. of isosceles triangle 3. Prop. of isosceles triangle 4. Substitution 5. Triangle Sum Property 6. Substitution 7. Addition 8. Subtraction Prop. of Equal. 9. Division Prop. of Equal. 10. Substitution 11. AA ~ Thm Note: SAS ~ Thm is another strategy. No scale factor information available. Statement 1. Angles F and H are right angles Reason Given Right angles are congruent Vertical Angles Theorem AA Similarity Theorem

5 Statement Reason Given 2. Vertical Angle Theorem 3. Ratios of corresponding sides Corresponding sides are related by the same scale factor 5. SAS ~ Thm The triangles are not similar. Not a common scale factor.

6 p o 38 o 57 o 95 o 28 o 57 o Similar?

7 15 35 o o 16 Similar? Y Similar? Y

8 Similar? N 83 o 34 o o 83 o 34 o o Similar? Y

9 PROOFS PRACTICE 1 Math 3 EO3 TOOLKITS Similarity

10 Temp.notebook October 09, 2017 TOOLKIT: Calculating Scale Factors Similar ~ triangles have: 1. Congruent angles. 2. Proportional sides (same scale factor). = Scale Factor > 1 Smaller to larger polygon side length of the larger polygon side length of the smaller polygon side length of the smaller = side length of the larger Scale Factor < 1 Larger to smaller polygon Examples: Scale Factors Large to small Small to large Solve for x: Scale Factors Large to small Small to large Solve for x: Scale Factors Large to small Small to large Solve for x: Scale Factors Large to small Small to large Solve for x: Parallel Lines Cut by a Transversal FOLDABLE TOOLKIT: polygon polygon

11 TOOLKIT: Angle Vocabulary Define the following terms. Diagrams would be helpful. Point identifies a position, has no dimension, labeled with a single capital letter Line determined by two points, infinite length, no thickness or width, labeled with two capital letters with a line above or one single lower case letter Plane a two-dimensional serface determined by 3 points, infinite length and width but no thickness, labeled with 3 capital letters or one italicized capital letter Angle two rays with a common starting point Angles can be named with numbers Angles can be named with letters. V U W Right Angle equals 90 degrees Y X Note that is not specific. It could be referring to any of 4 angles. Obtuse Angle greater than 90 degrees Acute Angle less than 90 degrees Straight Angle equals 180 degrees Adjacent Angles two angles with a common vertex and shared side (ray) Linear Pair adjacent angles whose measures add up to 180 degrees (supplementary) Vertical Angles two congruent angles formed by intersecting lines Complementary Angles 2 angles whose measures add up to 90 degrees Supplementary Angles 2 angles whose measures add up to 180 degrees Perpendicular Lines lines in a plane that intersect at 90 degree angles Parallel Lines lines in a plane do not intersect Transversal line that intersects parallel lines TOOLKIT: Properties of Similar Polygons See p166 Investigation 311 #5 All Isosceles right triangles are similar. All equilateral triangles are similar. All squares are similar. All rhombuses are NOT similar. All regular (all sides congruent) hexagons are similar...all regular n agons are similar.

12 TOOLKIT: Similarity Theorems #1 SAS Similarity Theorem! SAS ~ Thm #2 SSS Similarity Theorem! SSS ~ Thm #3 AA Similarity Theorem! AA ~ Thm NOTE: Why are ASA and SAA not included as similarity theorems??? ANSWER: When considering "sufficient conditions" we are looking for the minimum criteria that consistently proves similarity. Since we have proved AA as a similarity theorem, that's the minimum criteria. Both ASA and SAA add an additional criteria of a S (side). Can you see that both ASA and SAA have AA in them? TOOLKIT: Properties, Postulates, & Theorems Name Description Diagram Linear Pair Postulate Vertical Angles Theorem Angle Addition Postulate See p45 #13 Exterior Angle Theorem for a Triangle See p46 #15 Midpoint Connector Theorem for Triangles See p176 #5 Substitution Property of Equality Addition, p31 Subtraction, Multiplication or Division Property of Equality* Corresponding Angles Postulate Converse of the Corresponding Angles Postulate Alternate Interior Angles Theorem Converse of the Alternate Interior Angles Theorem Alternate Exterior Angles Theorem Converse of the Alternate Exterior Angles Theorem Same side Interior Angles Theorem Converse of the Same side Interior Angles Theorem Same side Exterior Angles Theorem Converse of the Same side Exterior Angles Theorem Reflexive property Two adjacent angles whose p31 unshared sides form a straight angle are supplementary (equal to 180 o) When two lines intersect, opposite angles that share the same vertex or corner point are p32 congruent. If P is a point in the interior of then An exterior angle of a triangle is equal to the sum of the two remote interior angles If the two midpoints of a triangle are connected, then the midline is parallel to and half the length of the third side. If the value of 2 quantities are know to be equal, then the value of one quantity can be replaced by the value of the other. Adding, subtracting, multiplying, or dividing* the same number from each side of an equation gives us an equivalent equation. *Pick just one operation! CAs are Congruent If two lines are intersected by a transversal and corresponding angles are congruent, then the lines are parallel. AIAs are Congruent If two lines are intersected by a transversal and alternate interior angles are congruent, then the lines are parallel. AEAs are Congruent If two lines are intersected by a transversal and alternate exterior angles are congruent, then the lines are parallel. SSIAs are Supplementary If two lines are intersected by a transversal and same side interior angles are congruent, then the lines are parallel. SSEAs are Supplementary If two lines are intersected by a transversal and same side exterior angles are congruent, then the lines are parallel. Congruent to itself B 180 o NOTE: We will add to this Toolkit as necessary. A P C or

13 TOOLKIT: Tips for Writing Similarity Proofs GIVEN: Could be in list, a sentence, or a diagram. PROVE: Typically four options Triangles are similar ~ Corresponding angles are congruent Sides are related by the same scale factor Lines are parallel STATEMENT 1. Proofs typically begin by stating the given information 1. Given REASON The body of the proof must lead to the similarity theorem that you're using: AA ~ Thm: Write statements & reasons that show that the two pairs of corresponding angles are congruent. SSS ~ Thm: Write statements & reasons that show that all corresponding sides are related by the same scale factor. SAS ~ Thm: Write statements and reasons that show that the two pairs of corresponding sides are related by the same scale factore and that the included angles are congruent. Your final statement must be exactly the same as what you're asked to prove in the prompt. If proving that triangles are similar, then your last statement is a similarity statement AA ~ Thm or SSS ~ Thm or SAS ~ Thm If proving that corresponding angles are congruent, then your last statement is an angle congurence statement. NOTE: You must have shown that the triangles are similar first, then you can use this reason! CASTC* (Corresponding Angles of Similar Triangles are Congruent) If proving that sides are related by the same scale factor, then your last statement is a scale factor statement where k NOTE: You must have shown that the triangles is the scale factor. are similar first, then you can use this reason! CSSTSSSF* (Corresponding Sides of Similar Triangles Share the Same Scale Factor) 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. Pick the reason that fits the proof Converse of the Corresponding Angles Postulate Converse of the Alternate Interior Angles Theorem Converse of the Alternate Exterior Angles Theorem Converse of the Same side Interior Angles Theorem Converse of the Same side Exterior Angles Theorem *CASTC and CSSTSSSF are the acronyms for the phrases in parenthesis. If you can recall the acronym correctly, then use it. If not, you need to write out a similarly worded reason.

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