Logical Reasoning in Geometry Unit 4 Logical Reasoning in Geometry

Pre Day- Vocabulary

Define these terms! Line Segment Perpendicular Lines Coplanar Midpoint Bisect Non-collinear Plane Parallel Lines Skew Lines Non-coplanar Collinear

Matching (in packet) Complete the matching activity Bring it up to the front to check answers when done Draw examples of each word in the blank space @ the bottom of the page in packet

Flip Book We’re going to make a flip book that looks just like the picture Each person needs 3 pieces of paper Every group needs 1 pair of scissors You will need something to write with. I recommend using a pencil for the inside and perhaps a marker for the outside tab

Flip Book Cover Page: Unit 4 FoM 3 Reasoning in Geometry Label each tab as follows: We will fill in the booklet each day Midpoint Complimentary Angles Segment Addition Postulate Perpendicular Bisector Angle Addition Postulate Vertical Angles Bisectors Supplementary Angles Perpendicular Lines Angles & Parallel Lines

Using Definition of Midpoint Day 1 Using Definition of Midpoint

Warm Up Day 1

Don’t assume midpoint! You must be told! Def: Midpoint The midpoint of a line segment divides the line segment into two congruent segments. A B M 1) 3) 5) 2) 4) 6) Don’t assume midpoint! You must be told!

Flipbook

Let’s do the evens!

Now you try the odds!

1.1 Guided Practice in packet Turn in Example 2 and Example 3 as ET on half sheet of paper before leaving

Segment Addition Postulate Day 2 Segment Addition Postulate

Warm Up Day 2

Let’s think… How would I measure the floor length of this classroom with a 12 inch ruler? I’d like 3 volunteers to measure please! That’s basically the segment addition postulate!

Addition and Subtraction of Line Segments: If several line segments belong to the same line, we can write addition and subtraction expressions using the names of these segments. R P S Geometry Leeson: Undefined Terms, Lines, Line Segments

Flipbook

1.2 Guided Practice Ex In packet!

Stations Complete the stations on a separate piece of paper and have them checked by me before you leave!

Angle Addition Postulate Day 3 Angle Addition Postulate

Warm Up Day 3 If Q is the midpoint of … 1) What is the value of x? 2) What is the measure of 3) What is the measure of ? Q

Review Naming Angles

Angle Addition Postulate First, let’s recall some previous information from last week…. We discussed the Segment Addition Postulate, which stated that we could add the lengths of adjacent segments together to get the length of an entire segment. For example: JK + KL = JL If you know that JK = 7 and KL = 4, then you can conclude that JL = 11. The Angle Addition Postulate is very similar, yet applies to angles. It allows us to add the measures of adjacent angles together to find the measure of a bigger angle… J K L

Angle Addition Postulate Slide 2 If B lies on the interior of ÐAOC, then mÐAOB + mÐBOC = mÐAOC. B A mÐAOC = 115° 50° 65° C O

Flipbook

A B C D G K H J 134° 46° 46 Given: mÐGHK = 95 mÐGHJ = 114. Example 1: Example 2: Slide 3 G 114° K 46° 95° 19° H This is a special example, because the two adjacent angles together create a straight angle. Predict what mÐABD + mÐDBC equals. ÐABC is a straight angle, therefore mÐABC = 180. mÐABD + mÐDBC = mÐABC mÐABD + mÐDBC = 180 So, if mÐABD = 134, then mÐDBC = ______ J Given: mÐGHK = 95 mÐGHJ = 114. Find: mÐKHJ. The Angle Addition Postulate tells us: mÐGHK + mÐKHJ = mÐGHJ 95 + mÐKHJ = 114 mÐKHJ = 19. Plug in what you know. 46 Solve.

Set up an equation using the Angle Addition Postulate. Given: mÐRSV = x + 5 mÐVST = 3x - 9 mÐRST = 68 Find x. Algebra Connection Slide 4 R V Extension: Now that you know x = 18, find mÐRSV and mÐVST. mÐRSV = x + 5 mÐRSV = 18 + 5 = 23 mÐVST = 3x - 9 mÐVST = 3(18) – 9 = 45 Check: mÐRSV + mÐVST = mÐRST 23 + 45 = 68 S T Set up an equation using the Angle Addition Postulate. mÐRSV + mÐVST = mÐRST x + 5 + 3x – 9 = 68 4x- 4 = 68 4x = 72 x = 18 Plug in what you know. Solve.

x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 C B mÐBQC = x – 7 mÐCQD = 2x – 1 mÐBQD = 2x + 34 Find x, mÐBQC, mÐCQD, mÐBQD. C B mÐBQC = x – 7 mÐBQC = 42 – 7 = 35 mÐCQD = 2x – 1 mÐCQD = 2(42) – 1 = 83 mÐBQD = 2x + 34 mÐBQD = 2(42) + 34 = 118 Check: mÐBQC + mÐCQD = mÐBQD 35 + 83 = 118 Q D mÐBQC + mÐCQD = mÐBQD x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 mÐBQC = 35 mÐCQD = 83 mÐBQD = 118 Algebra Connection Slide 5

1.3 Practice: Coach/Student One person is the coach, other is student Complete 1 & 2 Swap roles Complete 3 & 4 Reflect – which role was more difficult for you to fill? Why would that be true?

Exit Ticket – ½ sheet

Day 4 Bisectors

Warm Up Top section of Warm Up 1.4 in packet

Midpoint The point that bisects a segment. Bisects? splits into 2 equal pieces A M B 12x+3 10x+5 12x+3=10x+5 2x=2 x=1

Segment Bisector A segment, ray, line, or plane that intersects a segment at its midpoint. k A M B

Angle Bisector A ray that divides an angle into 2 congruent adjacent angles. BD is an angle bisector of <ABC. A D B C

Flipbook

Ex: If FH bisects EFG & mEFG=120o, what is mEFH?

Last example: Solve for x. * If they are congruent, set them equal to each other, then solve! x+40o x+40 = 3x-20 40 = 2x-20 60 = 2x 30 = x 3x-20o

1.4 Guided Practice

Day 5 Review and Quiz 4A

Warm Up Day 5 – round robin On your WU paper, copy your problem. Draw a picture if needed then set up an equation to solve. Pass your paper to left. Verify the equation, fix if needed. Then solve for x. Pass left. Verify value of x by plugging in, fix if needed. Then find lengths. Pass left. Check over all work, fix if needed. Kudos!

LMR - quiz

Day 6 Right Angles

Warm Up Day 6

Right Angles What are right angles? How are they formed? Why are they important? Find examples of right angles around the room.

Perpendicular Lines “Perpendicular lines are special intersecting lines that form right angles (square corners) where they intersect.”

Flipbook

1.5 Guided Practice in packet

Day 6 Angle Relationships

Warm Up Day 6

Flipbook

1-2-3-6-7-8 Work your assigned problem as a group You have 5 minutes Now Jigsaw around the room – become a master of all! Random members will share on board

Exit Ticket

Supplementary Angles and Linear Pairs Day 7 Supplementary Angles and Linear Pairs

Warm Up Day 7

Video on Supplementary Angles and Linear Pairs Watch me if you need a bit of help!

1.7 Guided Practice Musical Groups!

1.7 Practice Silent, individual practice today to ensure everyone in the classroom is confident!

Day 8 Parallel Lines

Warm Up Day 8 Solve for the numbered angles.

Parallel Lines and Transversals What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. Exterior Interior The symbol || is used to indicate parallel lines. Exterior AB || CD

Transversal A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. transversal Exterior Exterior transversal Parallel lines Non-Parallel lines Interior Interior Exterior Exterior

Corresponding Angles ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. Line M B A Line N D E L P Q G F Line L ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.

Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. Line M B A Line N D E L P Q G F Line L ÐBPQ = ÐDQP ÐAPQ = ÐEQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.

Exit Ticket 1. Name the angles congruent to 3. 1, 5, 7 2. Name all the angles supplementary to 6. In the figure a || b. 1, 3, 5, 7 3. If m1 = 105° what is m3? 105° 4. If m5 = 120° what is m2? 60°