# Dilations similarity and proportionality

Lane kim actressUse the ratio of similarity to form proportions. Find the value of an unknown using the product of the means and the product of the extremes ... – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 274295-NmIwY Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Day 1 – Dilations and Scale Factor Ratios in Similar Polygons 1. A similarity ratio is the ratio of the lengths of the _____ sides of two similar polygons. 2. Two polygons are similar if and only if their corresponding angles are _____ and their corresponding sides are _____. 3. Aligned with Chapter 7 of the Glencoe-McGraw Hill Geometry Textbook, this is a test over some of the tools of geometry including solving proportions, identifying similar figures, finding unknown sides of similar figures, and basic dilations. It was intended for a remedial high school geometry class, The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding Dilations and Similar Figures Have you ever wondered how different mirrors work? Most mirrors show you a reflection that looks just like you. But other mirrors, like the mirrors commonly found at carnivals and amusement parks, reflect back a face that is stretched or squished. You may look taller, shorter, wider, or narrower.

SRT-A: Understand similarity in terms of similarity transformations. Standards: SRT-A.1. Verify experimentally the properties of dilations given by a center and a scale factor: SRT-A.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. SRT-A.1.b. Dilations Similar Figures Similarity in Right Triangles. OH.Math.HSG.SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Similar Figures. OH.Math.HSG.SRT.B: Prove and apply theorems both formally and informally involving similarity using a variety of methods.

• Best place to farm world drops wowModule 6- Lesson 2 Triangle Dilations (A Solidify Understanding Task) Examining proportionality relationships in triangles that are known to be similar to each other based on dilations. 6.2 TASK 6.2 RSGs. Name: 65. Extend 7-1 Graphing Technology Lab: Fibonacci Sequence and Ratios - Analyze the Results 1. 2. 3. 4. 5.
• Geometry Module 2: Similarity, Proof, and Trigonometry. Just as rigid motions are used to define congruence in Module 1, so dilations are added to define similarity in Module 2. To be able to discuss similarity, students must first have a clear understanding of how dilations behave. Day 1 – Dilations and Scale Factor Ratios in Similar Polygons 1. A similarity ratio is the ratio of the lengths of the _____ sides of two similar polygons. 2. Two polygons are similar if and only if their corresponding angles are _____ and their corresponding sides are _____. 3.
• Music player appsStudents will use proportions to find the scale factor between them and use the scale factor to find unknown lengths of corresponding parts. Students will also analyze figures to determine if they are similar as well perform dilations and verify a figure is similar by its dilation.

dilations. Key Words • dilation • reduction • enlargement A is a transformation with center C and scale factor k that maps each point P to an image point P9 so that P9 lies on CP&*(and CP 9 5 k pCP. As you saw in the Geo-Activity above, a dilation maps a figure onto a similar figure, called the image. dilation 7.6 Dilations 5 Calculate ... 8.3 Proportionality. The student applies mathematical process standards to use proportional relationships to describe dilations. 8.3(A) generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation 8.3(B) compare and contrast the attributes of a shape and its dilation(s) on a CCSS.Math.Content.HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Mercury's core is different from any other planetary core in the Solar System. Earth has a metallic, liquid outer core sitting above a solid inner core. Mercury appears to have a solid silicate crust and mantle overlying a solid, iron sulfide outer core layer, a deeper liquid core layer,... corresponding sides are in proportion, and their angle measures are all the same. In other words, similar figures are the same shape but not necessarily the same size. Dilations create similar figures. The sides of similar figures must be in proportion; they must have the same: SCALE FACTOR! translations, and dilations of two-dimensional shapes on a coordinate plane. 8.10.C Explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation. Visit my.hrw.com to see all the unpacked. 332 Unit 5 Day 1 -Feb 6th - Intro to Similarity Learning Cards - Due Daily Lesson Notes: Click Here Day 2 -Feb 7th - Proportions and Shadow Math Lesson Notes: Click Here HW: Learning Cards 25, 26, 27 ... Capacitor bypass for op ampA dilation is a type of transformation that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is. Below is a picture of each type of dilation (one that gets larger and one that gest smaller). Example 1. The picture below shows a dilation with a scale factor of 2. Students will be apply to use properties of similar triangles, dilations, and triangle proportionality to solve problems. Agenda - opening problem (5 min) - do Similarity and Proportions quiz in groups of 3 (20 min) - go over Similar Triangles Unit Practice Test (5 min) practice test answer key - whiteboard problems on similarity and ... Transformations - Geometry Transformations Dilations Notes and Assignment This is a set of notes meant to teach the concept of the transformations created by Dilations. Included in this product your will find: A set of teacher notes that covers: ***** what is a dilation ***** what are the ... 5-6 Dilations LESSON Tell whether each transformation is a dilation. 1. 2. Dilate each figure by the given scale factor with the origin as the center of dilation. What are the vertices of the image? 3. scale factor of 2 4. scale factor of 1 2 A A A A x O y A DC B 8 6 4 2 4 6 O x 2 y A D C B 2 4 4 2 2 4 4 2 not a dilation dilation x O 4 4 2 2 y ... Day 1 – Dilations and Scale Factor Dilations as Proportions Ex) Rectangle CUTE was dilated to create rectangle UGLY. Find the length of LY. Ex) Determine which of the following figures could be a dilation of the triangle to the right. (There could be more than one answer) 3 in. 10 in. 1. Find the length of ABcc after the dilation. 2.

the face and body are still in proportion) Note: here we call it resizing , but other people call it dilation, contraction, compression, enlargement or even expansion ! Same idea, just different names. standard g.srt.a.2 GEO Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. QSC ID Skill Quantile Measure Resources; QSC343: Find the slope of a line given two points on a line, a table of values, the graph of the line, or an equation of the line in number and word problems.

Rigid motions and dilations are used to prove that two figures are similar, and they are the basis for developing triangle similarity criteria. The properties of dilations describe parallel relationships between corresponding line segments, collinear relationships between points, proportional relationships between lengths of corresponding line segments, and congruent relationships between corresponding angle measures. Dilations Scale Factor ... Notes on Scale Factor Similar Polygon Practice Scale Factor and Area Triangle Proportionality Notes 6.3 Triangle Proportionality WS . Describe that a dilation multiplies distances from the center of dilation to the original point by the scale factor to get the dilated point. Compare dilations with rigid transformations, explaining that dilations and rigid transformations preserve angle measures, but dilations result in proportional, not congruent, side lengths. When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1, &De Similar Triangles: Perimeters and Areas Solving Proportion Word Problems Involving Similar Figures Answer each question and round your answer to the nearest whole number. 1) If a 6 ft tall tent casts a 10 ft long shadow then how long is the shadow that a 9 ft tall adult elephant casts? 2) A model plane has a scale of 1 in : 6 yd. If the model plane is 3 in tall then how tall is the ... #7, with a center of dilation somewhere other than the origin will not be assessed. The Issaquah School District reserves the right to remove any user-generated content it deems inappropriate or not relevant to the topic of the forum. Name: 65. Extend 7-1 Graphing Technology Lab: Fibonacci Sequence and Ratios - Analyze the Results 1. 2. 3. 4. 5.

Notes on Dilations and Similarity Cluster 1: Understanding similarity in terms of transformations 5.1.1: Dilation with a center and scale factor, with a parallel line and a line segment 5.1.2: Transformations with similarity using equality of corresponding angles and proportionality of corresponding sides 5.1.3: Establish criterion of AA using ... 2) SSS similarity : If the corresponding sides of two triangles are proportional, then the two triangles are similar. * Translation keeps the triangle and its image congruent * Dilation keeps the measure of angles of the triangle and its image equal but the lengths of the corresponding side of it and its image are proportion Solving Proportion Word Problems Involving Similar Figures Answer each question and round your answer to the nearest whole number. 1) If a 6 ft tall tent casts a 10 ft long shadow then how long is the shadow that a 9 ft tall adult elephant casts? 2) A model plane has a scale of 1 in : 6 yd. If the model plane is 3 in tall then how tall is the ... Ratio, Proportion, and Similarity. Section 1: Ratio and Proportion . Section 2: Proportions Involving Line Segments. Section 3: Similar Polygons. Section 4: Proving Triangle Similar. Section 5: Dilations. Section 6: Proportional Relations Among Segments Related to Triangles. Section 7: Concurrence of the Medians of a Triangle Dilations Similar Figures Similarity in Right Triangles. OH.Math.HSG.SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Similar Figures. OH.Math.HSG.SRT.B: Prove and apply theorems both formally and informally involving similarity using a variety of methods.

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. the face and body are still in proportion) Note: here we call it resizing , but other people call it dilation, contraction, compression, enlargement or even expansion ! Same idea, just different names. c.You can prove that two figures are similar if you can show how to get from one image to the other through a series of transformations._____ d.A triangle that is rotated 180° and then dilated with a scale factor of 4 produces a congruent triangle. Similar Triangles Examples and Problems with Solutions. Definitions and theorems related to similar triangles are discussed using examples. Also examples and problems with detailed solutions are included.

In this lesson students will create a “2‐dilation” of a square and examine the characteristics and relationships of the square and its image. The data generated will be used to develop a conceptual understanding of similarity. Rationale Understanding similarity and proportionality and Geometry A - PLATO Math Notes/Videos ... GeoGebra CCSS.MATH.CONTENT.HSG.C.A.1 Prove that all circles are similar. CCSS.MATH.CONTENT.HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding ... A dilation is a non-rigid transformation, which means that the original and the image are not congruent. They are, however, similar figures. To perform dilations, a scale factor and a center of dilation are needed. If the scale factor is larger than 1, the image is larger than the original;

5-6 Dilations LESSON Tell whether each transformation is a dilation. 1. 2. Dilate each figure by the given scale factor with the origin as the center of dilation. What are the vertices of the image? 3. scale factor of 2 4. scale factor of 1 2 A A A A x O y A DC B 8 6 4 2 4 6 O x 2 y A D C B 2 4 4 2 2 4 4 2 not a dilation dilation x O 4 4 2 2 y ... Aligned with Chapter 7 of the Glencoe-McGraw Hill Geometry Textbook, this is a test over some of the tools of geometry including solving proportions, identifying similar figures, finding unknown sides of similar figures, and basic dilations. It was intended for a remedial high school geometry class, Day 1 – Dilations and Scale Factor Dilations as Proportions Ex) Rectangle CUTE was dilated to create rectangle UGLY. Find the length of LY. Ex) Determine which of the following figures could be a dilation of the triangle to the right. (There could be more than one answer) 3 in. 10 in. 1. Find the length of ABcc after the dilation. 2. **Dilation and Similarity Quiz in 2 Classes- Thursday, January 21st** 1/19/16 Day 46 CW: Similarity Through Dilation WS (first page) HW: Dilations Practice WS **Dilation and Similarity Quiz NEXT Class- Thursday, January 21st** Topics will include: -Proportions (Video tutorials) -Writing and solving proportions -Dilations (Video tutorials ...

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