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CCSS Geom Unit A Day 3 Seg AdditionA.notebook D.I.R.T? August 19, 2014 Day 3 Segment Addition Segment Addition Postulate Learning Targets: I can use the segment addition postulate to find the length of segments. I can apply the definition of congruent, midpoint, and bisect to find the length of segments. CCSS: GCO.1 CLE: N.2.D. Performance Standard 1.6, 3.4, 3.5 DOK1 Knowledge MA 3 Buddy Books today!!!! 1 CCSS Geom Unit A Day 3 Seg AdditionA.notebook August 19, 2014 PROPERTIES OF EQUALITY PROPERTIES OF EQUALITY ADDITION: If a=b, then a+c = b + c MULTIPLICATION: If a = b, then a c = bc SUBTRACTION: If a = b, then a c = b c DIVISION: If a = b, then a/c = b/c . (1) (2) PROPERTIES OF CONGRUENCE PROPERTIES OF CONGRUENCE REFLEXIVE: a = a TRANSITIVE: If a = b and b = c then a = c. . SYMMETRIC: If a = b then b = a SUBSTITUTION: If a=b you can replace one with the other. 2 CCSS Geom Unit A Day 3 Seg AdditionA.notebook PROPERTIES OF CONGRUENCE August 19, 2014 Other Properties DISTRIBUTIVE: a (b+c) = ab + ac Segment Addition: XY + YZ = YZ Angle Addition: m<AOB + m<BOC = m<AOC Vertical angles are congruent. Linear pairs are supplementary. Ruler postulate: The distance between any two points is measureable. A segment has two ENDPOINTS, therefore it can be MEASURED! Segment AB = 3 inches long A B If segments can be measured, then their lengths can be compared. If two segments have the same length then we say the segments are CONGRUENT. Congruent segments: two segments with the same length. Actual measurements are considered EQUAL not congruent. Use the congruent symbol with letters: Use the equal signs with numbers: 3 CCSS Geom Unit A Day 3 Seg AdditionA.notebook A B C D 8 5 2 0 3 August 19, 2014 E 1) Find AC. 2) Find BE. 3) Find CE. 4) AB ≅ ______. A BC≅ ______ AB = ______ 6 B C 4 CCSS Geom Unit A Day 3 Seg AdditionA.notebook August 19, 2014 Segment Addition postulate: If 3 points are collinear, then AB + BC = AC. C B A Do you see why you need to Know the Gab? An important fact of understanding geometric figures: coding and labeling!!! Mark all information in a figure that you understand from the information given. Examples: Label and code all information. Solve for the value(s). 5) A C CT= 10 AT=2 CA=? T 6) D 7) E S F T G DT=60 DS=2x8 ST=3x12 X= DS= DT= EF=2x6 FG=x+7 EG=25 x= EF= FG= 5 CCSS Geom Unit A Day 3 Seg AdditionA.notebook 8) Given AC = 36 August 19, 2014 3x 2x + 1 B A Statement Reason 1. AC = 36 1. Given 2. AB + BC = AC 2. 3. 3x + 2x + 2 = 36 4. 5x + 1 = 36 5. 5x = 35 6. x = 7 3. C 4. 5. 6. Segment addition Proofs 9) EG = 100, Find the value of x. Statement .E .F 4x20 2x + 30 .G Reason 6 CCSS Geom Unit A Day 3 Seg AdditionA.notebook August 19, 2014 Midpoint the point that divides a segment into two congruent segments. M is the midpoint of AB. Label and code. 10) D 11) P O G T Q O is the midpoint of DG. DO= 2x+11 OG=3x4 Find: DO= OG= DG= T is the midpoint of PQ. PT= 5x+3 TQ=7x9 Find PT. 12) C is the midpoint of AB. AC = 2x + 1 and CB = 3x 4. Find AC, BC and AB. Draw a picture and label. Show all work. Box answers. 7 CCSS Geom Unit A Day 3 Seg AdditionA.notebook August 19, 2014 Name the property of equality or congruence that justifies each statement 13) <K≅<K 14) If 2x8 = 10, then 2x = 18 15) If RS ≅ TW and TW ≅ PQ, then RS ≅ PQ 16) If m<A = m<B, then m<B =m<A What did you learn today? Can I use the segment addition postulate to find the length of segments? Can I apply the definition of congruent, midpoint, and bisect to find the length of segments? 8