8/11/2019 Eureka Math Grade 8 Module 2 Tips for Parents

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1Prepared by The Eureka Math 6-8 Writing Team

The Concept of Congruence

In this -lesson module, studentslearn about translations, reflections, androtations in the plane and how to usethem to precisely define the concept ofcongruence. Up to this point,congruence has been taken to mean,

intuitively, same size and same shape.Because this module begins a seriousstudy of geometry, this intuitivedefinition must be replaced by a precisedefinition. This module is a first step; itsgoal is to provide the needed intuitivebackground for the precise definitons thatare introduced in this module for the firsttime. Students are also introduced to thePythagorean Theorem.

Key WordsTransformation:A rule, to be denoted bthat assigns each point of the plane aunique point which is denoted by ().

Basic Rigid Motion: A basic rigid motion ia rotation, reflection, or translation of thplane.

Translation: A basic rigid motion thatmoves a figure along a given vector.

Rotation: A basic rigid motion that movesfigure around a point, degrees.

Reflection:A basic rigid motion that mova figure across a line.

Image of a point, image of a figure: Imarefers to the location of a point, or figureafter it has been transformed.

Sequence (Composition) ofTransformations:More than one transformation.

Vector :A Euclidean vector (or directedsegment)is the line segment together with a direction given byconnecting an initial point to a terminalpoint .

Congruence: A congruence is a sequence basic rigid motions (rotations, reflectionstranslations) of the plane.

Transversal: Given a pair of lines and

in a plane, a third line is a transversal if

intersects at a single point and intersec

at a single but different point.

GradeModuleEureka MathTips for Parents

What Came Before this Module:Students used their knowledge of

operations on numbers to include integerexponents and transformed expressions.Students made conjectures about how zeroand negative exponents of a number shouldbe defined and proved the properties ofinteger exponents.

What Comes After this Module:In Module , students learn about dilation

and similarity and apply that knowledge to aproof of the Pythagorean Theorem based onthe Angle-Angle criterion for similartriangles. Students learn the definition of adilation, its properties and how to composethem. One overarching goal of this module isto replace the common idea of same shape,different sizes with a definition of similaritythat can be applied to shapes that are not

polygons, such as ellipses and circles.

Describe, intuitively, what kind oftransformation will be required to move

Figure A on the left to its image on theright.

+ How Can You Help AtHome?

Every day, ask your child whatthey learned in school and askthem to show you an example.

Be excited to learn new ideas inmath! Show your child that mathis fun, even when it might be newand challenging!

Ask your child to describe atranslation, reflection androtation in his/her own words.

Watch the video posted belowwith your child and discuss eachof the transformations.http://www.youtube.com/watch?v=O2XPy3ZLU7Y

Key Common Core Standards: Understand congruence and similarity using physical models,

transparencies, or geometry software.o Verify experimentally the properties of rotations, reflections, and

translations:

Lines are taken to lines, and line segments to line segments ofthe same length.

Angles are taken to angles of the same measure.

Parallel lines are taken to parallel lines.

o Understand that a two-dimensional figure is congruent to another if thesecond can be obtained from the first by a sequence of rotations,reflections, and translations; given two congruent figures, describe asequence that exhibits the congruence between them.

o Use informal arguments to establish facts about the angle sum andexterior angle of triangles, about the angles created when parallel linesare cut by a transversal, and the angle-angle criterion for similarity oftriangles.

Understand and apply the Pythagorean Theorem.o Explain a proof of the Pythagorean Theorem and its converse.

o Apply the Pythagorean Theorem to determine unknown side lengths inright triangles in real-world and mathematical problems in two and

three dimensions.

Transformations in this module

Translation

Rotation

Reflection

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For more information visit commoncore.org

Grade Module

Below are two examples of the type of problems involvingreflectionsyour child will see in this unit. Spotlight on a

modelfrequently

used in thismodule:

Reflections

Sample Problem from Module 2:(Example taken from Module 2, Lesson 6)

Here is an example of a problem using rotations:

Use the diagram to the right for problems 1-5. Use your transparency as needed.

1. Looking only at segment BC, is it possible that a 180 rotation would map BConto BC? Whyor why not?

It is possible because the segments are parallel.

2. Looking only at segmentAB, is it possible that a 180 rotation would mapABonto AB? Whyor why not?

It is possible because the segments are parallel.

3. Looking only at segmentAC, is it possible that a 180 rotation would mapAConto AC? Whyor why not?

It is possible because the segments are parallel.

4. Connect point B to point B, point C to point C and point A to point A. What do you notice?What do you think that point is?

All of the lines intersect at one point. The point is the center of rotation. I checked by using my transparency.

5. Would a rotation map triangle ABConto triangle ABC? If so, define the rotation (i.e. degree and center). If notexplain why not.

Let there be a rotation 180 around point (0,-1). Then Rotation () = .

Problem: Given a right triangle with ahypotenuse with length 13 units and aleg with length 5 units, as shown,determine the length of the other leg.

= =

= =

= = =

Solution:Pythagorean Theorem

The length of the leg is

12 units.

A positive attitudetowards math is veryimportant in helpingyour child succeed inschool. In the ever-

changing world we livein, a strong foundationin math, paired withexcellent problem

solving skills may openmany doors for your

child in the years tocome!

ABC was reflected acrossline L. Notice how Point Band

line Ldid not move in thistransformation. Also, noticehow the image was labeledand how this is different fromthe original figure.

Figure Dwas also reflectedacross line L.