11 Congruence And Transformations - Glencoe
Lesson11Main IdeaUse a series oftransformations toidentify congruentfigures.Congruence and TransformationsYou can compare figures to determine if they are thesame size and shape.Copy the figure shown on tracingpaper two times. Cut out bothfigures. Label the figures A and B.Math OnlinePlace Figure B on top of Figure A.Are the figures the same?glencoe.comSlide Figure B up and over on your desk. Can youmove Figure A on top of Figure B so all sides andangles match?8.G.1, 8.G.1a, 8.G.1b,8.G.1c, 8.G.2Flip Figure B over. Can you move Figure A on top ofFigure B so all sides and angles match?In the activity above, you matched Figure A to Figure B by atranslation and a reflection. Two figures are congruent if the secondcan be obtained from the first by a series of rotations, reflections,and/or translations.Identify CongruencyDetermine if the two figures are congruent byusing transformations.BCYXAStep 1Reflect ABC over a vertical line.Label the vertices of the imageA , B , and C .ZBAB'C C'YXA'ZStep 2Translate A B C until all sides andangles match XYZ.C'XSo, the two triangles are congruent becausea reflection followed by a translation willmap ABC onto XYZ.B'YA'ZLesson 11 Congruence and Transformations45
Aa. Determine if the two figures are congruentby using transformations. Explain yourreasoning.TransformationsTranslations, reflectionsand rotations are calledisometries. In an isometry,the distance between twopoints in an image is thesame as the distance in thepreimage.iso / metryBDetermine if the two figures are congruentby using transformations.Reflect the red figure over a vertical line.same distanceBEven if the reflected figure is translated up andover, it will not match the green figure exactly.The two figures are not congruent.DACb. Determine if the two figures arecongruent by using transformations.Explain your reasoning.If you have two congruent figures, you can determine thetransformation, or series of transformations, that maps one figureonto the other by analyzing the orientation or relative position ofthe figures.TranslationReflectionRotation length is the same orientation is the same length is the same orientation is reversed length is the same orientation is changedNotice the segments arefacing the same way.Notice the segments arefacing the opposite way.Notice the segments arefacing a different way.BBAB'BAA'B'A'AB'A'
GRAPHIC DESIGN Ms. Martinez created the logoshown. What transformations did she use if theletter “d” is the preimage and the letter “p” isthe image? Are the two figures congruent?Step 1Start with the preimage. Determine whichtransformation will change the orientationof the letter.Step 2Rotations or reflections changeorientation. Rotate the letter “d” 180 about point A.Step 3iamondlumbingATranslate the new image up.ASo, Ms. Martinez used a rotation and translation to create the logo.The letters are congruent because images produced by a rotationand translation have the same shape and size.CheckTrace the letter “d” with tracing paper. Rotate the letter 180 around Point A. Slide it up to line up with the letter “p.” Theletters are the same shape and size. They are congruent c. GRAPHIC DESIGN What transformations could beused if the letter “W” is the preimage and theletter “M” is the image in the logo shown?Examples 1 and 2Determine if the two figures are congruent by using transformations.Explain your reasoning.1.L2.MZNYExample 3X3. LOGOS The Boyd Box Company uses the logo shown.What transformations could be used if the top, redtrapezoid is the preimage and the bottom, bluetrapezoid is the image?Lesson 11 Congruence and Transformations47
Examples 1 and 2Determine if the two figures are congruent by using transformations.Explain your reasoning.4.TSRUWZXS5.BAYTCR6.7.HPGFNMB8. STATIONERY Nilda purchased some custom printedstationery with her initials. What transformationscould be used if the letter “Z” is the preimage andthe letter “N” is the image in the design shown?N9. ART Simon is illustrating a graphic novel for a friend.He is using the two thought bubbles shown. Whattransformations did he use if Figure A is the preimageand Figure B is the image?A10. One way to identify congruent trianglesis to prove their matching sides have thesame measure. Triangle CDE has verticesat (1, 4), (1, 1), and (5, 1).a. Find the lengths of the sides of CDE.b. Reflect CDE over the y-axis, thentranslate it 2 units left. Label thevertices of the image C D E .c. Find the lengths of the sides of C D E .d. Are the two triangles congruent?Justify your response.NExample 3By65C4321-6 -5 -4 -3 -2-1 ODE1 2 3 4 5 6-1-2-3-4-5-6Find the lengths of the sides of the preimage with the given vertices andthe image after the transformations are performed. Then determine if thetwo figures are congruent.11. preimage: (0, 1), (4, 0), (4, 1)transformations: translate 3 units up then reflect over the y-axis12. preimage: (0, 0), (4, 0), (0, 4)transformations: reflect over the x-axis then dilate by a scale factor of 2x
C13. OPEN ENDED Create a design using a series of transformations thatproduce congruent figures. Exchange designs with a classmate anddetermine what transformations were used to create their design.14. CHALLENGE Angle ABC has points A( 3, 4), B( 2, 1) and C(2, 2).Find the coordinates of the image of the angle after a 90 clockwiserotation about the origin, a translation of 2 units up, and a reflectionover the y-axis.15. CHALLENGE Line segment XY has endpoints at X(3, 1) and Y( 2, 0).Its image after a series of transformations has endpoints at X (0, 1) and Y (5, 0). Find the series of transformations that maps XY onto X Y .Then find the exact length of both segments.16. WRITE MATH Explain why rotations, reflections, and translations createcongruent images.TTest Practice17.SHORT RESPONSE Gregory is creatinga mosaic for art class. He started byusing triangular tiles as shown.18. Triangle MNO is congruent to triangleRST.NMTRBOSAWhat are possible transformations heused if Figure A is the preimage andFigure B is the image?Which series of transformations maps MNO onto RST?A. 90 clockwise rotation about M thenreflectionB. translation then dilationC. 90 clockwise rotation about M thentranslationD. reflection then translation
The two figures are not congruent. b. Determine if the two figures are congruent by using transformations. Explain your reasoning. If you have two congruent figures, you can determine the transformation, or series of transformations, that maps one figure onto the other by analyzing the orientation or relative position of the figures.
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Geometry Student Notes 14 Section 4-4: Congruence and Transformations SOL: G.3.d Objectives: Identify congruent figures Describe congruence transformations Use theorems about congruence transformations Vocabulary: Congruent figures – figures are congruent, if and only if, there is a rigid motion or
Congruence – Congruent parts: ASA, AAS & HL Triangle Congruence Class Work If the triangles are congruent, state whether SSS, SAS, ASA, AAS, or HL applies and write congruence statement. ASA Congruence AC # XZ C # Z If ABC # XYZ by the given congruence, what is the missing congruent part? Draw and mark
Geometry Unit 2—Triangle Congruence Notes Triangle Congruence Theorems (SSS AND SAS) Practice: Mark the included side in each triangle Practice: Mark the included angle in each triangle. Side – Side – Side (SSS) Congruence Theorem Congruence Theorem three sides of one triangle are congr
Right Triangle Congruence Theorems Vocabulary Choose the diagram that models each right triangle congruence theorem. 1. Hypotenuse-Leg (HL) Congruence Theorem a. X Y Z Q R P 2. Leg-Leg (LL) Congruence Theorem b. U V X W 3. Hypotenuse-Angle
Unit 1: Congruence, Proof, and Constructions . Unit 1 embodies critical changes in Geometry as outlined by the AZCCRS. The heart of the module is the study of transformations and the role transformations play in defining congruence. In this unit, students will work with the relatively unfamiliar concept of construction.
Welcome to Reviewing Chemistry This workbook is designed to strengthen your knowledge of the NSCS (National Science Content Standards) and provide additional chapter content review of your Glencoe textbook, Chemistry: Matter and Change. For each chapter in the Glencoe textbook, Chemistry: Matter and Change, two pagesFile Size: 751KBPage Count: 56Explore furtherDownload Free Glencoe Chemistry: Matter and Change - drevquuosites.google.comChemistry Matter and Change - Glencoe - Chapter 7 .quizlet.comChemistry: Matter and Change - Chemistry Textbook .www.brightstorm.comRecommended to you based on what's popular Feedback
fresh garden produce, honey, jams, pickles and an assort-ment of other homemade goods. The market is located on 11th Street in downtown Glencoe across from the Glen-coe City Center. Glencoe seniors to meet The Glencoe Senior Citizens group will meet Thurs-day, Oct. 10, at 12:30 p.m., at the senior room in the Glencoe City Center.
