Math 1 Quarter 2 Overview

Transcription

1 Friday, November 18th EO9 Test Wednesday, November 30th Math 1 Quarter 2 Overview EO6 Modeling Quadratic Functions EO7 Solving Quadratic Functions EO8 Probability EO9 Understanding Congruence EO10 Properties of 2D and 3D Shapes EO6 Opp #1 EO7 Opp #1 EO8 Opp #1 EO9 Opp #1 Wed, Oct 26th Fri, Nov 4th Tue, Nov 15th Wed, Nov 30th ML ML ML EO6 Fri, Nov 4th EO7 Tue, Nov 15th EO8 Fri, Dec 2 EO9 Wed, Dec 7th EO10 Opp #1 Fri, Dec 9th Q2 Final Wed/Thu Dec 14/15 EO6 Opp #2 Tue, Nov 8th EO7 Opp #2 Thu, Nov 17th EO8 Opp #2 Tue, Dec 6th EO9 Opp #2 Mon, Dec 12th 1

2 Review p1 2 Review p3 4 11/14 EO8 Opp #1 Tue, Nov 15th EO9 Intro Worksheet Pythagorean Theorem and Its Converse EO7 Tue, Nov 15th? 11/15 11/16 11/17 11/ p363 #1, #3 and handout Triangle & Quadrilateral Inequality Practice Triangle & Quadrilateral Inequality Theorems 612 Triangle Congruence handout Triangle Congruence Maze A & B EO7 Opp #2 Thu, Nov 17th Triangle Congruency Theorems Billy Bob's Road Kill Cafe handout Triangle Congruence Maze A & B CYU p373 & OYO p384 #5 Pass back EO8 Test T H A N K S G I V I N G B R E A K Triangle Congruency Theorems Practice EO8 Friday Dec. 2nd EO8 Opportunity 2 is Tuesday Dec. 6th Block 1/2: Micaiah, Diego, Lizbeth, Bailey Missing: Jaelyn, Jess, Daniel Block 5/6: Sitlali, Cece, Brendon Missing: Aracely, Shawn 2

3 Let's practice with these Maze Activities :) Maze A Let's practice with these Maze Activities :) Maze B 3

4 Let's try another activity to make sure we know which are triangle congruency theorems and which are not! Billy Bob's Road Kill Cafe! USE CENTIMETERS INSTEAD OF INCHES! *a little tricky Check your triangles BEFORE you cut them out! Example: Each team needs to make all 7 sandwiches (split up the work. Each person does 1 2 sandwiches for the team!) USE CENTIMETERS INSTEAD OF INCHES! WHEN YOUR TEAM HAS HAD ALL 7 SANDWICHES CHECKED, CUT THEM OUT AND TAPE THEM UNDER THE APPROPRIATE HEADING ON THE BOARD! 4

5 WHY DON'T THESE ONES WORK? The angle in yellow can be small or big! The angle in yellow can be small or big! EO10 Congruence Practice 5

6 How did we do? Maze Activity Answers Maze A How did we do? Maze Activity Answers Maze B 6

7 2. Fill in the 3 parts that are given to you. Make sure they go in the right spot! c is always the longest side. If equal, then it's a right triangle. If NOT equal, then it's NOT a right triangle 2. Fill in the 3 parts that are given to you. Make sure they go in the right spot! c is always the longest side. If equal, then it's a right triangle. If NOT equal, then it's NOT a right triangle temp.notebook EO9 Congruence TOOLKITS Pythagorean Theorem & Its Converse Triangle Inequality Theorem Quadrilateral Inequality Theorem Triangle Congruency Theorems Proof CPCTC TOOLKIT: Pythagorean Theorem & Its Converse The Pythagorean Theorem: For a right triangle, the sum of the two leg lengths squared is equal to the length of the hypotenuse squared. a 2 + b 2 = c 2 a b c The Pythagorean Theorem can be used to find any missing side of a RIGHT triangle so long as two sides of the triangle are known. Examples: Find the hypotenuse: Find the leg: The Converse of the Pythagorean Theorem: For a any triangle with sides a, b, c, if a 2 + b 2 = c 2, then it's a right triangle? 1. Write a 2 + b 2 = c 2 2. Fill in the 3 parts that are given to you. Make sure they go in the right spot! c is always the longest side. 3. Solve each side of the equation. If equal, then it's a right triangle. If NOT equal, then it's NOT a right triangle 4. Write your answer in a complete sentence Asking the question "Is it true?" Example #1? 1. Write a2 + b2 = c2 Example #2? 1. Write a2 + b2 = c2 13in 12in 3. Solve each side of the equation. 5cm 7cm 3cm 3. Solve each side of the equation. 5in 4. Write your answer in a complete sentence 4. Write your answer in a complete sentence 7

8 TOOLKIT: Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the third side length. Examples: a c b Activity #2: Can these side lengths form a triangle? Quadrilateral? Explain. 1) 5, 7, 13 4) 3, 5, 7, 13 2) 6, 12, 9 5) 12, 6, 9, 25 3) 25, 10, 15 6) 24, 2, 14, 8 TOOLKIT: Quadrilateral Inequality Theorem The sum of any three side lengths of a quadrilateral is greater than the fourth side length. Examples: Can form a quadrilateral 5 2 a 5 b d 12 Cannot form a quadrilateral c 3 8

9 TOOLKIT: Triangle Congruency Theorems Triangles have 3 angles and 3 side lengths. To prove that triangles are congruent, you must show that there are 3 congruent parts. A C B F D E Y Z X CONGRUENT FIGURES All corresponding sides and all corresponding angles are congruent (equal)! ΔABC ΔDEF ΔXYZ AB DE XY AC DF XZ BC EF YZ <A <D <X <B <E <Y <C <F <Z So, how many combinations of angles and sides are possible? Six! S.A.S. S.S.S. A.A.S. A.S.A. H.L So, it must be a right triangle to have an hypotenuse! But two of them can NEVER be used to prove congruence. S.S.A A.A.A Be careful to recognize that the order of these letters represents the shortest consecutive path around the triangle. Do you understand??? 9