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Name: Date:Geometry Quad. Proof Review

Answer each of the following questions in groups. Each group will be selected to make a poster of two proofsand present their solutions to the class.

(1) Given the quadrilateral ABCD with its vertices at A (3, -5), B (5, 1), C (1, 4), and D (-5, 1). Prove whether or

not ABCD is an isosceles trapezoid.

(2)Given: ABCD is a parallelogram,

Prove: AECD is an isosceles trapezoid

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(3)Given: ABCD is a parallelogram,

Prove:

(4)Given: ABCD is a parallelogram,

,

Prove: DEFC is a rectangle

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(5) In parallelogram ABCD, AB = x + 4, DC = 3x 36, and BC = 2x -16. Show that ABCD is a rhombus.

(6) In parallelogram ABCD, AE = 7x 1, and EC = 5x +5. a.a. Find AC.b. If DB = 10x +10, find DBc. What kind of parallelogram is ABCD? Why?

(7) The measures of angles A and B of parallelogram ABCD are in the ratio 2:7. Find the measure of angle A.

(8) In parallelogram ABCD, BC = 9y+10, AD = 6y + 40, AB = y +50. Find BC, AD, AB, and DC.

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(9) Prove that Quadrilateral ABCD with vertices, A (1, 1), B (3, -2), C (4, 1), D (2, 4) is a parallelogram.

(10) Prove that Quadrilateral ABCD, with vertices A (0, 0), B (5, 0), C (5, -6), D (0, -6) is a rectangle.

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esson Title: Proof Me a Quadrilateral

eacher Name: Ryan Bischofubject: Geometry Grade Level: 10th grade

me Required (days; time/day): 2-3 Most work will be done outside class.opic: Quadrilateral Proof Review

ssential Question: How to determine if a quadrilateral is a square, rectangle, rhombus, etc. using the Geometryoof.

re-requisites (Prior Knowledge): Triangle proof theorems and strategies.

Quadrilateral proof theorems and strategies.

Proof techniques.

Graphing, distance formula, slope formula, and midpoint formula.

STAGE 1 - DESIRED RESULTS

Content Area Standard(s): (include complete standard, not just standard #)

YS Standards of Mathematics:

G.RP .2 Recognize and verify, where appropriate, geometric relationships ofperpendicularity, parallelism, congruence, and similarity, using algebraic strategies

G.RP.9 Apply inductive reasoning in making and supporting mathematical conjectures

G.RP.4 Provide correct mathematical arguments in response to other studentsconjectures, reasoning, and arguments

G.G.41 Justify that some quadrilaterals are parallelograms, rhombuses, rectangles,squares, or trapezoids

etrieved from http://www.emsc.nysed.gov

echnology Standards:

acilitate and Inspire Student Learning and Creativity

eachers use their knowledge of subject matter, teaching and learning, and technology to facilitatexperiences that advance student learning, creativity, and innovation in both face-to-face and virtual

nvironments. Teachers:

Promote, support, and model creative and innovative thinking and inventiveness.

Engage students in exploring real-world issues and solving authentic problems using digital tools asources.

Promote student reflection using collaborative tools to reveal and clarify students' conceptualnderstanding and thinking, planning, and creative processes.

Model collaborative knowledge construction by engaging in learning with students, colleagues, andhers in face-to-face and virtual environments.

etrieved from http://www.iste.org

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Intended Learning Outcome Define what students will know and be able to do and at what level of mastery theyhould be able to do it. NOTE: Add/subtract rows from below each column heading,

Student will know Student will be able to

roperties of a parallelogram. Prove each quadrilateral is a parallelogram, rectangle, rhomor square using different proof methods.

roperties of a rectangle. Categorize the quadrilateral, given certain properties, using traditional geometry proof.

roperties of a rhombus. Using a coordinate proof and the distance, midpoint, and sloformulas to categorize the given quadrilateral with givenproperties.

roperties of a square.oordinate proof techniques.

stance, midpoint, and slope formulas.

STAGE 2 - ASSESSMENT EVIDENCE

tudents will demonstrate their learning/understanding in the following way(s):

Teacher-Created Assessments:re-test:

eacher will create a survey on the class wiki reviewoncepts about quadrilateral proofs. Students willg on and vote for the correct answers.or example:

Give one method to prove a quadrilateral is asquare.

What can a I show in a coordinate proof toprove the quadrilateral is a rhombus?

If I prove the quadrilateral has two pairs ofparallel sides, what is the quadrilateral?

Post-test:

Students will work collaboratively in groups using goggle doand prezi.

Students will work in groups to solve three proofs usigoggle docs to work out the proofs at home.

Each group will work collaboratively and input theirproofs into a class prezi on Quadrilateral proofs, creaand reviewed by the teacher.

One student will receive extra credit for polishing up prezi and creating the path for the presentation thefollowing day.

Performance Assessments: Students will be graded on their portion of the class prezi using a gradingbric.

Other Assessments (e.g., Peer, Self): The project grade will also include a rubric for self-assessment andeer assessment.

Assessment Adaptations:STAGE 3 - LEARNING PLAN

Learning ActivitiesInstructional Strategies/Learning Activities:

.g., demonstration, discussion, small groups, role play, etc.)udents will create their own Wordle for a single quadrilateral, using concepts and definitions from the Quadrilateraroofs Unit. Students will print them out overnight. Following day students will switch with a partner and figure outhich quadrilateral the Wordle is about.

Introducing the Lesson: (capturing students attention, activating students prior knowledge).udents and teacher will work out a triangle proof together as review/activating their prior knowledge.

Instructional Sequence:epresenting the content: teaching/learning activities, connecting to students prior knowledge, etc.) Complete thellowing two columns, showing teacher activity in correspondence with student activity. Add/subtract rows as neede

Teacher activity (The teacher is doing.) Student activity (The student is doing)

Pair students up with their Wordles and have theudents decipher which quadrilateral their partnersordle depicted.

1. Students will create their Wordles as homework from thenight before.

Group pairs of students into groups of four byombining the pairs with different Wordle

2. Students will exchange Wordles and determine whichquadrilateral their partner chose.

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uadrilaterals.

Each group will be given all the proofs, but willnly be asked to complete four of the proofs.umber of proofs may vary by the number of groups.

3. Students will be given the proof questions and given fourproofs to work on and solve.

Students will be walked through how to make aoogle doc and will be given the invite for the classezi (which they will have used already).

4. During class or at home, students will work in Google dorepresent their proofs digitally.

As students work, the teacher will aid studentsth google docs and prezi if needed. 5. Students will take their collaborative proofs from theirrespective google docs and import them into prezi and add ithe class prezi. Each group will add two proofs to the prezi.

Teacher will monitor the prezi overnight and makeure the students are not having any issues throughe class wiki. The teacher will also make sure theath works smoothly on the prezi.

6. Students will present their part of the prezi to the class foevaluation.

Teacher will evaluate the presentations thelowing day.

7. Students will fill out a self-assessment and peer assessm

Adaptations to the Instructional Sequence to Differentiate:needed, demonstrations with google docs and prezi.airing students of high achievement with students who struggle.

Discussion and Assessment of Learning: (Pointing out to students how what they are learning is related to theiving question; assessing students learning as a result of the lesson)e will think and discuss different places or instances where you might use quadrilaterals and the proof thinkingrategy.

Closure:

1. Overall Closure Plans: The students will present their section of the class prezi and take outlines of the proofsey did not complete during the presentations and review them for the following day.2. Extensions for Early Finishers: Students who finish early will be asked to help groups who may be strugglingternatively, students who finish early may be given an extra intensive proof for extra credit if presented.3. Alternate strategies for struggling students or those who learn differently:ready established procedures such as the wiki, Edmodo, or their group members will be used.Procedures: (both already established procedures to be used, and procedures to be taught for this lesson)

oogle docs, Prezi, Edmodo, the class wiki, and their fellow group members.LESSON DEVELOPMENT RESOURCES

Technology Tools and Materials: (classroom set-up, preparations, resources, etc.)omputer lab with smart board.

Parent/Community Resources: Contact Information: School Email, Phone

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Student Sample Work

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Example Student Prezi with one proof: http://prezi.com/ebp9pabyh84c/student-example-for-retro-project/

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http://prezi.com/ebp9pabyh84c/student-example-for-retro-project/http://prezi.com/ebp9pabyh84c/student-example-for-retro-project/

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Rubrics

Comments:

20Point

s:

Eachproofw

ascompleteandfreefromerrors.Each

proofwasthoroughlycompletedandprovedinalo

gical

fashion.Correctnotationandwordingwasusedfo

r

eachproof.Mathematicallysound.

Name:

Assignment:

10Points:

Notypographical

errorsandattention

todetail.Prezisetup

inlogicalorder.

Teacher:

10Points:

Presentationwascompleteand

free

oferrors.Questionswere

ans

weredwhenapplicable.

Eac

hmemberplayedarolein

the

presentation.

GroupName:

5Points:

Overall

Self-Rating:

Date

:

5Points:

OverallPeer

Rating:

Overall

Rating:

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0

Self-EvaluationCommen

ts:

Strengths:

Weaknesses:

CollaborativeProcess:

Suggestionstoimproveactivity:

Checkoneofthefollowingscoresbelow.Behone

st,itwillbe

comparedtoyourgroup

membersratingofyou!

Name:

1

Date:

2

Teacher:

3

Assignment:

4

5

Group

Name:

12

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Group

Member4:

Group

Member3:

Group

Member2:

Group

Member1:

0 0 0 0

Peer-EvaluationComments:(Checkoneofthefollowingscoresforeach

groupmembe

rbelow.Behonest,itwillbecomparedtoyourse

lf-

evaluation!)

Comments:

Name:

1 1 1 1

Date:

2 2 2 2

Teacher:

3 3 3 3

Assignment:

4 4 4 4

5 5 5 5

Gro

up

Nam

e:

13