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High school geometry
Course: high school geometry > unit 3.
- Getting ready for congruence
- Congruent shapes & transformations
- Non-congruent shapes & transformations
Congruence & transformations
- Segment congruence equivalent to having same length
- Angle congruence equivalent to having same measure
- (Choice A) One more transformation — a rotation — would map △ A B C onto △ F E D . So the triangles are congruent. A One more transformation — a rotation — would map △ A B C onto △ F E D . So the triangles are congruent.
- (Choice B) One more transformation — a reflection — would map △ A B C onto △ F E D . So the triangles are congruent. B One more transformation — a reflection — would map △ A B C onto △ F E D . So the triangles are congruent.
- (Choice C) There is no error. This is a correct conclusion. C There is no error. This is a correct conclusion.
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Unit 2 – Transformations, Rigid Motions, and Congruence
Transformations
LESSON/HOMEWORK
LESSON VIDEO
EDITABLE LESSON
EDITABLE KEY
Reflections
Isosceles Triangles
Translations
Congruence and Rigid Motions
Basic Rigid Motion Proofs
Congruence Reasoning with Triangles
Symmetries of a Figure
Unit Review
Unit 2 Review – Transformations, Rigid Motions, and Congruence
UNIT REVIEW
EDITABLE REVIEW
Unit 2 Assessment Form A
EDITABLE ASSESSMENT
Unit 2 Assessment Form B
Unit 2 Assessment Form C
Unit 2 Assessment Form D
Unit 2 Exit Tickets
Unit 2 Mid-Unit Quiz (After Lesson #5) – Form A
Unit 2 Mid-Unit Quiz (After Lesson #5) – Form B
Unit 2 Mid-Unit Quiz (After Lesson #5) – Form C
Unit 2 Mid-Unit Quiz (After Lesson #5) – Form D
U02.AO.01 – 2 Kites (Enrichment)
EDITABLE RESOURCE
U02.AO.02 – Congruence and Rigid Motion Practice
U02.AO.03 – Isosceles Triangles – Extra Practice
U02.AO.04 – Polygon Symmetry and Mapping – Extra Practice
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TRANSFORMATIONS AND CONGRUENCE WORKSHEET
Question 1 :
A triangle has the vertices (3, 4), (5, 4) and (5, 2). Apply the indicated series of transformations to the triangle. Each transformation is applied to the image of the previous transformation, not the original figure. Label each image with the letter of the transformation applied.
(i) Reflect across the x-axis.
(ii) Translate 3 units to the left.
(iii) Reflect across the y-axis.
(iv) Translate 4 units up.
(v) Rotate of 90 ° clockwise about the origin.
Compare the size and shape of the final image to that of the original figure.
Question 2 :
Which transformations change the orientation of figures ?
Question 3 :
Which transformations do not change the orientation of figures ?
Question 4 :
Two figures have the same size and shape. What does this indicate about the figures ?
1. Answer :
Step 1 :
Since there is a reflection across the x-axis, we have to multiply each y-coordinate by -1. That is,
(x, y) -----> (x, -y)
So, we have
(3, 4) -----> (3, -4)
(5, 4) -----> (5, -4)
(5, 2) -----> (5, -2)
Graph the image.
Step 2 :
Since there is a translation of 3 units to the left , we have to subtract 3 from each x-coordinate. That is,
(x, y) -----> (x-3, y)
(3, -4) -----> (0, -4)
(5, -4) -----> (2, -4)
(5, -2) -----> (2, -2)
Since there is a reflection across the y-axis, we have to multiply each x-coordinate by -1. That is,
(x, y) -----> (-x, y)
(0, -4) -----> (0, -4)
(2, -4) -----> (-2, -4)
(2, -2) -----> (-2, -2)
Since there is a translation of 4 units up , we have to add 4 to each y-coordinate. That is,
(x, y) -----> (x, y+4)
(0, -4) -----> (0, 0)
(-2, -4) -----> (-2, 0)
(-2, -2) -----> (-2, 2)
(v) Rotate of 90° clockwise about the origin.
Since there is a rotation of 90° clockwise about the origin , we have multiply each x-coordinate by -1 and interchange x and y coordinates. That is,
(x, y) -----> (y, -x)
(0, 0) -----> (0, 0)
(-2, 0) -----> (0, 2)
(-2, 2) -----> (2, 2)
They have the same size and shape, just a different orientation.
2. Answer :
Reflections and rotations
3. Answer :
Translations
4. Answer :
One figure is the image of the other, and there is a sequence of transformations that will transform one figure into the other.
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Course 3 • Chapter 8 Transformations and Congruence Lesson 4 Problem-Solving Practice Congruence and Transformations Determine if the two figures are congruent by using transformations. Explain your reasoning. 1. 2. 3. The community softball team has created the following logo for their jerseys. What transformations could be
Practice for lesson 4-1 congruence Learn with flashcards, games, and more — for free.
to move it 4 units to the right and 5 units up. What are the coordinates of the vertices of the new pool? y O x 4. In the game of checkers, the pieces are set up in a particular order. Which transformation would place checker A on top of checker B? A B 5. Corinne is designing a quilt patch by using a coordinate plane. She begins by drawing the ...
Moevement of a figure from one location to another without a change in size, shape, or orientation. transformation in which a figure turns around a fixed point called the center of rotation. Rigid Motion. Study with Quizlet and memorize flashcards containing terms like Transformation, rigid motion, pre-image and more.
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.
1. Apply the transformation M : (x, y) →(3x, 3y) to the polygon with vertices D(1, 3), E(1, -2), and F(3, 0). Name the coordinates of the image points. Identify and describe the transformation. An isometry is a transformation that preserves length, angle measure, and area.
You can identify congruent fi gures in the coordinate plane by identifying the rigid motion or composition of rigid motions that maps one of the fi gures to the other. Recall from Postulates 4.1-4.3 and Theorem 4.1 that translations, refl ections, rotations, and compositions of these transformations are rigid motions. EXAMPLE 1.
Theorem. Theorem 4.2 Refl ections in Parallel Lines Theorem. If lines k and m are parallel, then a refl ection in line k followed by a refl ection in line m is the same as a translation. If A′′ is the image of A, then. 1. AA′′ — is perpendicular to k and m, and. 2. AA′′ = 2d, where d is the distance between k and m.
Unit 2 Mid-Unit Quiz (After Lesson #5) - Form A. ASSESSMENT. ANSWER KEY. EDITABLE ASSESSMENT. EDITABLE KEY.
They are congruent. A transformation that changes the size of an object, but not the shape. Two adjacent angles that form a straight line. A transformation that "flips" a figure over a mirror or reflection line. A line that acts as a mirror so that corresponding points are the same distance from the mirror.
TRANSFORMATIONS AND CONGRUENCE WORKSHEET. Question 1 : A triangle has the vertices (3, 4), (5, 4) and (5, 2). Apply the indicated series of transformations to the triangle. Each transformation is applied to the image of the previous transformation, not the original figure. Label each image with the letter of the transformation applied.
Lesson 1 Homework Practice Congruence and Transformations DATE PERIOD Determine if the two figures are congruent by using transformations. Explain your reasoning. c 5. GRAPHIC DESIGN The Art Club designed the logo shown. What transformations did they use if the top trapezoid is the preimage and the bottom trapezoid is the image? 6.
UNIT 2 Transformations and Congruence LESSON 4 Properties of Transformations Properties of Transformations Practice Complete this assessment to review what you've learned. It will not count toward your grade. A square with side $6 units in length is reflected across the x-axis.
Lesson 4 Learning Focus. Explore and justify triangle congruence criteria using rigid transformations. Lesson Summary. In this lesson, we learned that it is not necessary to know that all pairs of corresponding angles and sides are congruent before we can claim that two triangles are congruent.
4 Transformations 4.1 Translations 4.2 Reflections 4.3 Rotations 4.4 Congruence and Transformations 4.5 Dilations 4.6 Similarity and Transformations Revolving Door (p. 195) Kaleidoscope (p. 196) Magnification (p. 213) Chess (p. 179) Magnification (p. 213) Kaleidoscope (p 196) Revolving Door (p 195) SEE the Big Idea Chess (p. 179) Photo Stickers Photo Stickers (p. 211)(p. 211)
the graph of an object before a transformation. image. a figure that results from the transformation of a geometric figure. congruence transformation. also called a rigid transformation or an isometry, one in which the position of the image may differ from that of the pre-image, but the two figures remain congruent. reflection.
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor Self-Check Quizzes. Common Core State Standards Supplement, SE Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Online Calculators Study to Go. Mathematics. Home > Chapter 4 > Lesson 7. Illinois Geometry. Chapter 4, Lesson 7 ...
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor Self-Check Quizzes. Common Core State Standards Supplement, SE Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Study to Go Online Calculators. Mathematics. Home > Chapter 4 > Lesson 7. Indiana Geometry. Chapter 4, Lesson 7: Congruence ...
Section 11.4 Congruence and Transformations 569 11.4 Congruence and Transformations Refl ections in Parallel Lines Work with a partner. Use dynamic geometry software to draw any scalene triangle and label it ABC. a. Draw any line ⃖DE ⃗ Refl ect ABC in ⃖DE ⃗ to form A′B′C′. b. Draw a line parallel to ⃖DE ⃗ Refl ect
Determine if the two figures are similar by using transformations. Explain your reasoning. 1. E F G W Y X 2. R Q S NO QP T 3. H IJ Q P O 4. EW SL H G MR Lesson 3 Skills Practice Similarity and Transformations yes; Sample answer: A rotation and a dilation with a scale factor of 2 maps EFG onto XYW. yes; Sample answer: A rotation and a dilation ...
100 Course 3 • Chapter 7 Congruence and Similarity ... oduce for c lassr oom use. Lesson 1 Skills Practice Congruence and Transformations Determine if the two figures are congruent by using transformations. Explain your reasoning. 1. G F E H L K J M 2. T S U W Y X 3. TU WX V 4. B A CR S Q P D 5. EF PQ NS O R CH D G 6. Q LO T R S MN
Section 4.4 Congruence and Transformations 201 Congruence Transformations Another name for a rigid motion or a combination of rigid motions is a congruence transformation because the preimage and image are congruent. The terms "rigid motion" and "congruence transformation" are interchangeable. Describing a Congruence Transformation
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples Personal Tutor Self-Check Quizzes. Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Study to Go Online Calculators. Mathematics. Home > Chapter 4 > Lesson 7. Oklahoma Geometry. Chapter 4, Lesson 7: Congruence Transformations. Extra Examples; Personal ...