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<h3 class="wp-block-heading">Key Concepts</h3>



<ul class="wp-block-list">
<li>Understanding dilation</li>



<li>Describing dilation</li>



<li>Understanding similarity</li>



<li>Describing similarity</li>
</ul>



<h2 class="wp-block-heading"><strong>Dilation and Transformations </strong></h2>



<p><a href="https://www.turito.com/learn/math/compose-transformation-grade-8" data-type="link" data-id="https://www.turito.com/learn/math/compose-transformation-grade-8">Transformation</a>, different transformation, rigid transformation. </p>



<ul class="wp-block-list">
<li>Transformation is a change.&nbsp;</li>



<li>Translation is a transformation where the image or point slides across the plane.&nbsp;</li>



<li>Reflection is a transformation where the image flips across the line, and that line is called the line of reflection.&nbsp;</li>



<li>Rotation is a transformation that occurs around a fixed point, and that point is called the center of rotation.&nbsp;</li>



<li>Transformations in which there are no changes of size or shape after transformation are rigid transformations.&nbsp;</li>



<li>Translation, reflection, and rotation are examples of rigid transformation.&nbsp;</li>
</ul>



<h3 class="wp-block-heading">Understanding Dilation&nbsp;</h3>



<p>A dilation is a transformation that produces an image that is of the same shape and different sizes.&nbsp;Dilation that creates a larger image is called enlargement.&nbsp;</p>



<ul class="wp-block-list">
<li>Dilation that creates a smaller image is called reduction.&nbsp;</li>



<li>Center of dilation is the fixed point on the plane.&nbsp;</li>



<li>Scale factor is the ratio between the length of the original image to the transformed image.&nbsp;</li>



<li>Dilation is not a rigid transformation as it preserves only the shape.&nbsp;</li>



<li>Zooming can be given as an example of dilation.&nbsp;</li>
</ul>



<h3 class="wp-block-heading">Describing Dilation&nbsp;</h3>



<p><strong>Dilation of scale factor 2</strong>&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="304" height="315" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-998.png" alt="Dilation of scale factor 2 " class="wp-image-15700" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-998.png 304w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-998-290x300.png 290w" sizes="auto, (max-width: 304px) 100vw, 304px" /></figure></div>


<p>The following figure undergoes a dilation with a scale factor 2 giving an image A’ (2, 4), B’ (6, 6), &nbsp;<br>C’ (8, 2).&nbsp;</p>



<p><strong>D: (X,Y)</strong> <strong>&nbsp;</strong><img loading="lazy" decoding="async" width="108" height="27" class="wp-image-15724" style="width: 75px" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1017.png" alt=""><strong>(2x , 2y)</strong>  <strong>A(1,2), B(3,3), C(4,1)</strong>&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="311" height="311" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-997.png" alt="figure undergoes a dilation" class="wp-image-15699" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-997.png 311w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-997-300x300.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-997-150x150.png 150w" sizes="auto, (max-width: 311px) 100vw, 311px" /></figure></div>


<h2 class="wp-block-heading"><strong>Characteristics of Dilation&nbsp;</strong></h2>



<p>Each angle of the figure and its image remains the same.&nbsp;</p>



<ul class="wp-block-list">
<li>Midpoint of the sides of the figure remains the same as the midpoint of the dilated shape.&nbsp;</li>



<li>Parallel and perpendicular lines in the figure remain the same as the parallel and perpendicular lines of the dilated image.&nbsp;</li>



<li>The image remains the same.&nbsp;</li>



<li>If the scale factor is greater than 1, the image stretches.&nbsp;</li>



<li>If the scale factor is between 0 and 1, the image shrinks.&nbsp;</li>



<li>If the scale factor is 1, then the original image and the dilated image are congruent.&nbsp;</li>
</ul>



<h3 class="wp-block-heading">Similarity&nbsp;</h3>



<p>Two figures are said to be similar if their corresponding angles are congruent, and the ratio of the length of the corresponding sides is proportional.&nbsp;&nbsp;</p>



<p>The ratio of the perimeters is the same as the scale factor of similar triangles.&nbsp;</p>



<p>The scale factor for similar figures is a: b and the ratio of their areas is the scale factor squared: &nbsp;<br>a<sup>2</sup><sup> </sup>: b<sup>2</sup>.&nbsp;</p>



<p>The following figures are similar because the ratio of the length of corresponding sides is proportional, the scale factor is 2.&nbsp;</p><div class="fillWidthInMob"><a loading='lazy' class="showAdInAllRes"  data-toggle="modal" data-target=#homeLeadForm data-heading="Get Expert Guidance" href="#"><img class="img-fluid" alt="parallel" src=https://a.storyblok.com/f/128066/1100x230/00b28b4876/11-applying-for-collages_leaderboard-1100x230.jpg /></a></div>


<div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="293" height="183" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-999.png" alt="Similarity" class="wp-image-15701"/></figure></div>


<p class="has-text-align-center"><em>In similar triangles, corresponding angles are congruent.</em>&nbsp;</p>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1002.png" alt="All corresponding angles are equal " class="wp-image-15704" style="width:342px;height:257px" width="342" height="257" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1002.png 692w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1002-300x225.png 300w" sizes="auto, (max-width: 342px) 100vw, 342px" /></figure></div>


<p class="has-text-align-center"><em>All corresponding angles are equal</em>&nbsp;</p>



<p>Check whether the following figures are similar; if so, describe the similarity.&nbsp;</p>



<p>AB = 72, BC = 48, AC = 84&nbsp;</p>



<p>HG = 12, GF = 8, HF = 14&nbsp;</p>



<div class="wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex">
<div class="wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:50%"><div class="wp-block-image">
<figure class="aligncenter size-full"><img loading="lazy" decoding="async" width="199" height="174" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1000.png" alt=" figures are similar; if so, describe the similarity." class="wp-image-15702"/></figure></div></div>



<div class="wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow" style="flex-basis:50%">
<figure class="wp-block-image size-full"><img loading="lazy" decoding="async" width="195" height="174" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1001.png" alt=" figures are similar; if so, describe the similarity." class="wp-image-15703"/></figure>
</div>
</div>



<p>AB/HG = 72/12 = 6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>



<p>BC/GF = 48/8 = 6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>



<p>AC /HF = 84/14 = 6&nbsp;</p>



<p>The corresponding sides of the figure are proportional, so the triangles are similar.&nbsp;</p>



<h3 class="wp-block-heading"><strong>Key Concept Covered</strong>&nbsp;</h3>



<ul class="wp-block-list">
<li>Understand dilation&nbsp;</li>



<li>Describe dilation&nbsp;</li>



<li>Understand similarity&nbsp;</li>



<li>Describe similarity&nbsp;</li>
</ul>



<h2 class="wp-block-heading"><strong>Exercise</strong></h2>



<ol class="wp-block-list" type="1">
<li>State whether a dilation with the given scale factor is an enlargement or a reduction.</li>
</ol>



<p>a. &nbsp;Scale factor = 2,&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;b. &nbsp;Scale factor =1/8,&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c. &nbsp;Scale factor = 5/4</p>



<ol class="wp-block-list" start="2">
<li>Graph the image of rectangle KLMN after dilation with a scale factor of 4, centered at the origin.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1010.png" alt=" KLMN after dilation" class="wp-image-15713" style="width:328px;height:287px" width="328" height="287" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1010.png 524w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1010-300x263.png 300w" sizes="auto, (max-width: 328px) 100vw, 328px" /></figure></div>


<ol class="wp-block-list" start="3">
<li>Draw a dilation of scale factor 3.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1011.png" alt="dilation of scale factor 3." class="wp-image-15714" style="width:344px;height:306px" width="344" height="306" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1011.png 464w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1011-300x267.png 300w" sizes="auto, (max-width: 344px) 100vw, 344px" /></figure></div>


<ol class="wp-block-list" start="4">
<li>Find the vertices of the dilated image and describe it as enlargement or reduction. D : (x, y) (2x, 2y)</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1012.png" alt="enlargement or reduction. D : (x, y) (2x, 2y)" class="wp-image-15715" style="width:406px;height:308px" width="406" height="308" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1012.png 595w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1012-300x228.png 300w" sizes="auto, (max-width: 406px) 100vw, 406px" /></figure></div>


<ol class="wp-block-list" start="5">
<li>Scale factor of A to B is 1:9. Find the missing perimeter.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1013.png" alt="Scale factor of A to B is 1:9" class="wp-image-15716" style="width:357px;height:226px" width="357" height="226" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1013.png 470w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1013-300x190.png 300w" sizes="auto, (max-width: 357px) 100vw, 357px" /></figure></div>


<ol class="wp-block-list" start="6">
<li>The scale factor of two regular octagons is 4:1. Find the ratio of their perimeters and the ratio of their areas.</li>



<li>Find the missing length. The triangles in each pair are similar.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1014.png" alt="missing length" class="wp-image-15717" style="width:513px;height:179px" width="513" height="179" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1014.png 705w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1014-300x105.png 300w" sizes="auto, (max-width: 513px) 100vw, 513px" /></figure></div>


<ol class="wp-block-list" start="8">
<li>Solve for <em>x</em>. The triangles in each pair are similar.</li>
</ol>


<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1015.png" alt="triangles in each pair are similar." class="wp-image-15718" style="width:279px;height:209px" width="279" height="209" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1015.png 551w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1015-300x225.png 300w" sizes="auto, (max-width: 279px) 100vw, 279px" /></figure></div>

<div class="wp-block-image">
<figure class="aligncenter size-full is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1016.png" alt="triangles in each pair are similar 2" class="wp-image-15719" style="width:288px;height:269px" width="288" height="269" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1016.png 495w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1016-300x281.png 300w" sizes="auto, (max-width: 288px) 100vw, 288px" /></figure></div>


<h3 class="wp-block-heading"><img loading="lazy" decoding="async" width="75" height="69" class="wp-image-15711" style="width: 60px" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1008.png" alt=""><strong>What have we learned:</strong></h3>



<ul class="wp-block-list">
<li>What is a dilation?</li>



<li>Dilation is a transformation that changes its size without changing the shape.</li>



<li>What is a scale factor?</li>



<li>The scale factor in dilation is the number multiplied by each side length of the original figure to get the length of the side of the image after transformation.</li>



<li>What is similarity?</li>



<li>Similarity of two figures can be defined as the figures that undergo changes in size without changing the shape of the figure.</li>



<li>What is the criteria for identifying two similar triangles?</li>



<li>In similar triangles, there is a proportionality between the corresponding sides and corresponding angles are congruent.</li>
</ul>



<h3 class="wp-block-heading"><strong>Concept Map</strong>&nbsp;</h3>


<div class="wp-block-image">
<figure class="aligncenter size-large is-resized"><img loading="lazy" decoding="async" src="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1009-1024x587.png" alt="Concept Map " class="wp-image-15712" style="width:434px;height:248px" width="434" height="248" srcset="https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1009-1024x587.png 1024w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1009-300x172.png 300w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1009-768x440.png 768w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1009-1536x880.png 1536w, https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-1009.png 1562w" sizes="auto, (max-width: 434px) 100vw, 434px" /></figure></div>