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Geometry 27 January 2014WARM UP1) Complete Using Congruent Triangles handout2) Place Khan video notes on top of group folderFINISHED? Work on Geometry Proof Practice
Review- Triangle Congruency Shortcuts SSS, SAS but not SSA SAA (AAS), ASA but not AAACPCTC- corresponding parts of congruent triangles are congruent!
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Objective
Students will be able to prove and apply polygon properties.
HOMEWORK- DUE FRIDAY pg. 283: 1 – 6; pg. 304: 7 – 12; pg. 300: 1, 3, 4 Properties of Parallelograms HandoutUNIT 5 TEST- FRIDAY We will NOT have time to go over homework questions before the test.ANSWERS will be posted Wed/Th– see me w/ ?’s
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Complete Properties of QUADRILATERALS Handout
Think- Fill in as many properties of sides/ angles/ diagonals as you can
PAIR- TRADE- trade with a partner– do you see more they need to add? Use a different color.
SHARE- whole class review
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Definition of kite
• A kite is a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
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Properties of Kites
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Properties of Trapezoids
Consecutive angles between the bases are supplementary.
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Base angles of isosceles trapezoids are congruent. ⦟P S and Q ⦟ ⦟ R⦟
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Isosceles Trapezoids
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if a quadrilateral is a parallelogram
opposite sides are parallel (DEFINITION)opposite sides are congruentopposite angles are congruentconsecutive angles are supplementarydiagonals bisect each other
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Rhombus PropertiesRhombuses share all properties of a parallelogram AND:(1) Consecutive sides of a rhombus are congruent.(2) The diagonals of a rhombus bisect pairs of opposite angles.(3) The diagonals of a rhombus are perpendicular.
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Rectangle Properties
All properties of a parallelogram AND:• Diagonals are congruent• All angles are congruent (90⁰)
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deductive reasoning
the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts.
Inductive reasoning allows you to discover new ideas based on observed patterns.
Deductive reasoning can help explain why your conjecture is true.
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Got Proof?Logically step by step– what is true? why? statement reasonTHREE styles- flowchart, two-column, paragraph
Let’s practice– Complete Geometry Proof Practice HandoutFIRST- MARK the diagram with GIVEN information and HIDDEN congruencies!!
Be ready to present your work to the class.
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WHOLE CLASS
• Complete Properties of Polygons Handout SKETCHES and Conjectures for Parallelograms
FINISHED? do the proof on the back
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Debrief
What is easy?What still might be confusing to some students?
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Geometry 28 January 2014WARM UP- on your pink sheet1) Find m T⦟ 2)
FINISHED?Work on geometryProof Practice
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Objective
Students will be able to prove and apply polygon properties.
HOMEWORK- DUE FRIDAY pg. 283: 1 – 6; pg. 304: 7 – 12; pg. 300: 1, 3, 4 Properties of Parallelograms HandoutUNIT 5 TEST- FRIDAY We will NOT have time to go over homework questions before the test.ANSWERS will be posted Wed/Th– see me w/ ?’s
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Review 1: Trapezoids
What is x?
a) 5 b) 24 c) 48
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Review 2
In a rectangle ABCD, if AB = 7x – 3, and CD = 4x + 9, then x = ___ (strategy– draw a sketch)
A) 1B) 2C) 3D) 4E) 5
7x – 3 = 4x + 9-4x -4x 3x – 3 = 9 + 3 +3 3x = 12 x = 4
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Review 3
• The perimeter of a square MNOP is 72 inches, and NO = 2x + 6. What is the value of x?A) 15B) 12C) 6D) 9E) 18
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FLOW CHART PROOF1. Restate given information clearly. Mark the information on a sketch. Write the given information on the left.2. State what you are trying to show.3. Fill in the other boxes working backwards
and forwards as needed.4. ARROWS are used to connect information
directly resulting from a previous statements.
Thinking FLOWS left to right.
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a
1. Given: parallelogram SOAK with diagonal
Show: SOA AKS S
K A
O
3 4
SOAK is a parallelogram
SA
13
42
SO KA
Def. of parallelogram
?OA 1 2
AIA
?SA
GIVENDef of parallelogram
KS
AIA
SA
same segment
SOA AKS
ASA
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KHAN Quiz
Work silently. Do your best.
FINISHED? Work on Geometry Proof PracticeFINISHED? Work on 5.3 et. al. handout
Be ready to present your work to the class.
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Debrief
What is easy?What might still be confusing to some students?
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Geometry 29/ 30 January 2014
EMPTY Group Folders1) Look over your work from last week on the
“Four Pentagons” Problem2) Correct or finish your work as needed Please RESPOND to the prompts I wrote on your paper. You may use the 2nd clean sheet to re-work the problem as needed.
FINISHED? DO HW pblm pg. 300, #4.
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Objective
Students will be able to prove and apply polygon properties.
HOMEWORK- DUE FRIDAY pg. 283: 1 – 6; pg. 304: 7 – 12; pg. 300: 1, 3, 4 Properties of Parallelograms HandoutUNIT 5 TEST- FRIDAY We will NOT have time to go over homework questions before the test.ANSWERS will be posted Wed/Th– see me w/ ?’s
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Review Chapter 5 Quiz 2
What errors did you make?CORRECTONS for up to ½ credit accepted through February 6. Follow pink slip guidelines!
DISCUSS- Parallelogram Proofs on Geometry Proof Practice
REVIEW- Khan Quiz from yesterday
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PQRS is an isosceles trapezoid. Find m<P, m<Q, and m<R.
S R
P Q
50°
>
>
m<R= 50⁰
m<Q= m<P= 180 – 50 = 130º
check: 2(50) + 2(130) = 100 + 260 = 360√
base angles are congruent consecutive
angles are supplementary
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REVIEW 1
a =x= y=
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Review 2
• Find m<AA) 65°B) 135°C) 100°D) 90°E) 105°
AB
C
D
165°30°
65°
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Review 3
• Opposite angles of a parallelogram must be _______.A) complementaryB) supplementaryC) congruentD) A and CE) B and C
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Review 4
• If a quadrilateral has four equal sides, then it must be a _______.A) rectangleB) squareC) rhombusD) A and BE) B and C
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Review 5
• The perimeter of a square MNOP is 96 inches, and NO = 2x + 6. What is the value of x?A) 15B) 12C) 9D) 6E) 3
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Review 6
• ABCD is a trapezoid. Find the length of midsegment EF.A) 5B) 11C) 16D) 8E) 22
A
B
CD
E
F
11
5
9
13
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Review 7
• The quadrilateral below is most specifically a __________.A) rhombusB) rectangleC) kiteD) parallelogramE) trapezoid
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Summarize Properties of Quadrilaterals
Mark/ briefly summarize properties of each quadrilateral on handout. REMEMBER- each shape has ALL the properties of the classification above it.
Quadrilateral
Kite Parallelogram Trapezoid
Rhombus Rectangle
Square
Isosceles Trapezoid
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Let’s PRACTICE
COMPLETE 5.3 Handout for classwork.SOME answers are posted.
Be ready to present your work.
FINISHED? Begin Instructional Task: Applying Angle Theorems- Four Pentagons
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Debrief
What do you need to do to be ready for the test on Friday?
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Geometry Unit 5 TEST31 January 2014
Do you best. Work silently.
You have the whole period to complete the test.READ the problems carefully.SHOW supporting work for ALL PROBLEMS!!!HOMEWORK DUE SUNDAY- KHAN ASSIGNMENT
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TEST postponed due to low attendance
HOMEWORK QUESTIONS?
Polygon Properties Practice- Practice Handout White Board Review