9.5/10.3 CONGRUENT FIGURES VS. SIMILAR FIGURES ESSENTIAL QUESTIONS: 9.5 HOW CAN TRANSFORMATIONS BE USED TO VERIFY THAT TWO FIGURES HAVE THE SAME SHAPE.

Slides:

Advertisements

Similar presentations

Transformations Vocabulary.

Advertisements

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Adapted from Walch Education 1.4.1: Describing Rigid Motions and Predicting the Effects 2 Rigid motions are transformations that don’t affect an object’s.

Properties of Dilations

Properties of Dilations, Day 2. How do you describe the properties of dilations? Dilations change the size of figures, but not their orientation or.

Introduction Rigid motions can also be called congruency transformations. A congruency transformation moves a geometric figure but keeps the same size.

Unit 7 Lesson 8.7: Dilations

Objectives Define and draw lines of symmetry Define and draw dilations.

Transformations. There are four types –Translations –Reflections –Rotation –Dilation.

Term Transformation Describe The change in the position of a geometric figure, the pre-image, that produces a new figure called the image Representation.

An operation that moves or changes a geometric figure (a preimage) in some way to produce a new figure (an image). Congruence transformations – Changes.

6.7.1 Perform Similarity Transformations.  Remember previous we talked about 3 types of CONGRUENCE transformations, in other words, the transformations.

Similar Figures, Day 2. Warm Up Two figures are similar if one can be obtained from the other using a sequence of transformations in the plane.

Translations. Definitions: Transformations: It is a change that occurs that maps or moves a shape in a specific directions onto an image. These are translations,

TRANSFORMATIONS Objective:  To identify isometries  To find reflection images of figures.

4-1 Congruence and transformations. SAT Problem of the day.

Lesson 2.7 Objective: To complete dilations on a coordinate plane.

Dilations. Transformation – a change in position, size, or shape of a figure Preimage – the original figure in the transformation Image – the shape that.

Dilations Advanced Geometry Similarity Lesson 1A.

Transformations on the Coordinate Plane Mr. J. Grossman.

1.4 Rigid Motion in a plane Warm Up

CONGRUENCE AND TRANSFORMATIONS (GET GRAPH PAPER WHEN YOU ENTER CLASS) SECTION 4.4.

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Vocab 1 Vocab 2 Transformations CompositionsMiscellaneous.

4-7 Congruence Transformations. A transformation is an operation that maps an original geometric figure, the preimage, onto anew figure called the image.

Section 8.7 Dilations OBJECTIVE: TO UNDERSTAND DILATION IMAGES OF FIGURES BIG IDEAS:TRANSFORMATIONS COORDINATE GEOMETRY ESSENTIAL UNDERSTANDING: A SCALE.

EQ: How can you use transformations to determine if two shapes are congruent? Demonstrated in writing in summary of notes. Warm-Up Reflect this triangle.

 A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another.

UNIT 10 NOTES Dilations. Rigid Transformations ⇢ Congruence Reflections Rotations Translations Compositions Isometry!!!!!

Properties of Rotations 8.G.1, 8.G.3 Essential Question? How do you describe the properties of rotation and their effect on the congruence and orientation.

Transformations What’s it all about?.

Defining Similarity (5.3.1)

Do Now Find the value of every missing variable:.

Similarity and Transformations

Composition of Isometries & Dilations

State the new coordinates after performing the dilation (3x, 3y).

Defining Congruence in Terms of Rigid Motions

Module 11 So Far… Dilation is a transformation that makes an image that is the same shape, but may be a different size “Length” could be side length or.

Properties of Translations

Transformations Learning Target: I will be able to translate, reflect, rotate, and dilate figures.

Properties of Reflections

Reflections & Rotations

Copy the reflection and rotation chart 2 times each!!!!!

Introduction Think about resizing a window on your computer screen. You can stretch it vertically, horizontally, or at the corner so that it stretches.

Triangle Congruence Unit 1: Day 8

If f(x) = 2x−5, then what is the value of f(2) + f(5) ?

Mod 16.1: Dilations Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? CASS: G-SRT.1a, G-SRT.2b.

Similar Figures Essential Question?

4.1: Congruence and Transformation

Introduction Rigid motions can also be called congruency transformations. A congruency transformation moves a geometric figure but keeps the same size.

9-6 Dilations 9-7 Similarity Transformations

Triangle Congruence Unit 1: Day 8

Students will be able to define and apply translations.

Congruence and Similarity pg. 87

9-6 Dilations 9-7 Similarity Transformations

Congruence Transformations

Transformations, Congruence, and Similarity

11.6 Congruence and Transformations

Congruence and Similarity pg. 87

Investigating Properties of Parallelism and the Center

Similar Figures Essential Question?

Bell Ringer A figure has vertices A(2,2), B(6,4), C(-2,3), and D(-1,5). The image of this figure is a rotation of 90° clockwise. What is A’? What is.

Defining Similarity (5.3.1)

Congruent Figures Day 2.

Presentation transcript:

9.5/10.3 CONGRUENT FIGURES VS. SIMILAR FIGURES ESSENTIAL QUESTIONS: 9.5 HOW CAN TRANSFORMATIONS BE USED TO VERIFY THAT TWO FIGURES HAVE THE SAME SHAPE AND SIZE? 10.3 – WHAT IS THE CONNECTION BETWEEN TRANSFORMATIONS AND THE ORIENTATIONS OF SIMILAR FIGURES? If two figures are similar, then there exists a sequence of translations, reflections, rotations, and/or dilations that transforms one figure into another. If two figures have the same shape and size, then there exists a sequence of translations, reflections, and/or rotations that transforms one figure into another.

RECALL… The lines ______ and ________of pre-images and images have the same ________ and measure under a translation, reflection and rotation. Two figures are considered __________ if one can be obtained by either a translation, reflection, or rotation. Congruent figures have the same __________________ If you are told that two figures are congruent, there must be a ____________(order that the transformation occurred) of translations, rotations, and reflections that took place. sides angles lengths congruent size and shape sequence

PROPERTIES OF CONGRUENCY If a shape is __________, then the shapes are no longer __________. It changes the __________of the shape, which means the new image is no longer congruent to the pre-image. Since not all figures are congruent, you need to ______the sequence of translations, reflections and rotations that occurred. dilated length congruent prove

HOW TO FIND THE SEQUENCE Ask yourself … ? Did the orientation change? Did the _______ change? If so, HOW? Did a ________ occur? If so, HOW? How about a _________? If so, HOW? To identify sequence …. use the ___________________ we learned about and put the sequence of events in the order it occurred. position rotation reflection coordinate notation

PROPERTIES OF SIMILARITY Two figures are _________ if one can be obtained from the other by a sequence of translations, reflections, rotations, and __________. Similar figures have the same _________, but may be different __________. Similar figures can be _________ where congruent figures ________. similar dilations shape sizes dilated cannot

Type of Transformation p SizeShape Orientation (direction) Position ReflectionNever AlwaysSometimes RotationNever AlwaysSometimes TranslationNever Always Enlargement (Dilation) AlwaysNever Sometimes Reduction (Dilation)AlwaysNever Sometimes