6. Q6e
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Similar Question 1
<p>Which type(s) of triangles will always be similar: right, isosceles, or equilateral?</p>
Similar Question 2
<p>In the diagram shown, <code class='latex inline'>\angle ABC = 90^{\circ}</code>, <code class='latex inline'>CB \parallel ED</code>, <code class='latex inline'>AB = DF, AD = 24, AE = 25</code> and O is the centre of the circle. Determine the perimeter of <code class='latex inline'>CBDF</code>.</p><img src="/qimages/5401" />
Similar Question 3
<p>The triangles in each pair are similar. Find the unknown side lengths. </p><img src="/qimages/2363" />
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Determine the length of <code class='latex inline'>DB</code>.</p><img src="/qimages/1009" />
<p>Suppose that <code class='latex inline'>\triangle PQR</code> ~ <code class='latex inline'>\triangle LMN</code> and <code class='latex inline'>\angle P = 90^{\circ}</code>?</p><p>If <code class='latex inline'>MN=13</code> cm, <code class='latex inline'>LN=12</code> cm, <code class='latex inline'>LM=5</code>cm, and <code class='latex inline'>PQ=15</code> cm, what are the lengths of <code class='latex inline'>PR</code> and <code class='latex inline'>QR</code>?</p>
<p>Find the length of <code class='latex inline'>x</code> in each.</p><img src="/qimages/2364" />
<p>In the figure, <code class='latex inline'>RS</code> is perpendicular to <code class='latex inline'>PQ</code>, <code class='latex inline'>PS = 4</code>, and <code class='latex inline'>QS = 6</code>. Find the exact length of <code class='latex inline'>RS</code>.</p><img src="/qimages/327" />
<p>Refer to Question 1. </p><p>a) Find the area of each triangle. </p><p>b) How are these areas related?</p><p>c) How do the areas help to confirm that the triangles are similar?</p><p>Question 1</p><p>A right triangle has side lengths 3 cm, 4 cm and 5 cm. </p><p>a) Draw the triangle. </p><p>b) A similar triangle has hypotenuse 30 cm long. What is the scale factor? </p><p>c) What are the lengths of the legs?</p>
<p>A right triangle has side lengths 3 cm, 4 cm and 5 cm. </p><p>a) Draw the triangle. </p><p>b) A similar triangle has hypotenuse 30 cm long. What is the scale factor? </p><p>c) What are the lengths of the legs?</p>
<p>If two isosceles triangles have one pair of equal angles, are they similar? Explain.</p>
<p>a) Show why <code class='latex inline'>\triangle</code>PQR is similar to <code class='latex inline'>\triangle</code>STR. </p><p>b) Find the lengths <code class='latex inline'>x</code> and <code class='latex inline'>y</code>.</p><img src="/qimages/2359" />
<p>Determine the value of each lower-case letter. If you cannot determine a value, explain why.</p><img src="/qimages/1004" />
<p>Find the length of <code class='latex inline'>x</code> in each.</p><img src="/qimages/2367" />
<p><code class='latex inline'>\triangle</code>GHI<code class='latex inline'>\sim\triangle</code>KLM. Find the are of <code class='latex inline'>\triangle</code>KLM</p><img src="/qimages/2368" />
<p>The areas of two similar triangles are <code class='latex inline'>36 cm^2</code> and <code class='latex inline'>100 cm^2</code>. What is the ratio of the lengths of their corresponding sides?</p>
<ul> <li>Explain why you can conclude that <code class='latex inline'>\triangle ACB ~ \triangle EDB</code> in the diagram.</li> <li>Determine the scale factor that relates these triangles.</li> </ul> <img src="/qimages/1011" />
<p><code class='latex inline'>\triangle</code>PQR<code class='latex inline'>\sim\triangle</code>STU. Find the area of <code class='latex inline'>\triangle</code>PQR</p><img src="/qimages/2365" />
<p>Which triangles are similar to, but not congruent to, <code class='latex inline'>\triangle ABC</code>?</p><img src="/qimages/995" />
<p><strong>i)</strong> For the pair of right triangles, determine whether the triangles are congruent, similar, or neither.</p><p><strong>ii)</strong> If the triangles are congruent, identify the corresponding angles and sides that are equal. If the triangles are similar, identify the corresponding angles that are equal, and calculate the scale factor that relates the smaller triangle as a reduction of the larger triangle.</p><p> <img src="/qimages/996" /></p>
<p>Determine the value of each lower-case letter.</p><img src="/qimages/1008" />
<p><code class='latex inline'>\triangle</code>ABC<code class='latex inline'>\sim\triangle</code>STU. Find the are of <code class='latex inline'>\triangle</code>ABC</p><img src="/qimages/2366" />
<ul> <li>Suppose that <code class='latex inline'>\triangle PQR</code> ~ <code class='latex inline'>\triangle LMN</code> and <code class='latex inline'>\angle P = 90^{\circ}</code>. What angle in <code class='latex inline'>\triangle LMN</code> equals <code class='latex inline'>90^{\circ}</code>? </li> </ul> <p>How do you know?</p>
<p>The triangles in each pair are similar. Find the unknown side lengths. </p><img src="/qimages/2361" />
<p>Is <code class='latex inline'>\triangle ABC</code> ~ <code class='latex inline'>\triangle DEF</code>? Justify your answer.</p><img src="/qimages/2408" />
<p>Brett needs to support a radio tower with guy wires. Each guy wire must run from the top of the tower to its own anchor 9.00 m from the base of the tower. When the tower casts a shadow that is 9.00 m long, Brett’s shadow is 0.60 m long. Brett is 1.85 m tall. What is the length of each guy wire that Brett needs?</p><img src="/qimages/9925" />
<p>Are these two triangles similar? </p><img src="/qimages/1000" />
<p>The triangles in each pair are similar. Find the unknown side lengths. </p><img src="/qimages/2363" />
<p>Determine the value of each lower-case letter.</p><img src="/qimages/1006" />
<p>Determine the value of each lower-case letter.</p><img src="/qimages/1007" />
<p>The triangles in each pair are similar. Find the unknown side lengths. </p><img src="/qimages/6808" />
<p><strong>i)</strong> For the pair of right triangles, determine whether the triangles are congruent, similar, or neither.</p><p><strong>ii)</strong> If the triangles are congruent, identify the corresponding angles and sides that are equal. If the triangles are similar, identify the corresponding angles that are equal, and calculate the scale factor that relates the smaller triangle as a reduction of the larger triangle.</p><p> <img src="/qimages/999" /></p>
<p>a) Draw a scalene triangle.</p><p>b) Draw a scalene triangle that is</p> <ul> <li><p>congruent to the one you drew</p></li> <li><p>similar to the one you drew</p></li> <li><p>neither congruent nor similar to the one you drew</p></li> </ul>
<p>Refer to Question 1. </p><p>a) Find the area of each triangle. </p><p>b) How are these areas related?</p><p>Question 1</p><p>A right triangle has side lengths 3 cm, 4 cm and 5 cm. </p><p>a) Draw the triangle. </p><p>b) A similar triangle has hypotenuse 30 cm long. What is the scale factor? </p><p>c) What are the lengths of the legs?</p>
<p>The triangles in each pair are similar. Find the unknown side lengths. </p><img src="/qimages/2360" />
<p>Explain why you can conclude that <code class='latex inline'>\triangle ACB ~ \triangle EDB</code> in the diagram.</p><img src="/qimages/1011" />
<p>Calculate the heights of the two ramp supports, x and y. Round your answers to the nearest tenth of a metre.</p><img src="/qimages/9924" />
<p>In the diagram shown, <code class='latex inline'>\angle ABC = 90^{\circ}</code>, <code class='latex inline'>CB \parallel ED</code>, <code class='latex inline'>AB = DF, AD = 24, AE = 25</code> and O is the centre of the circle. Determine the perimeter of <code class='latex inline'>CBDF</code>.</p><img src="/qimages/5401" />
<p>The areas of two similar triangles are <code class='latex inline'>64 cm^2</code> and <code class='latex inline'>36 cm^2</code>. What is the ratio of the lengths of their corresponding sides?</p>
<p>A tree that is 3 m tall casts a shadow that is 2 m long. At the same time, a nearby building casts a shadow that is 25 m long. How tall is the building?</p>
<p>Determine the value of each lower-case letter.</p><img src="/qimages/1005" />
<p>Determine the value of each lower-case letter. If you cannot determine a value, explain why.</p><img src="/qimages/1002" />
<p>Two trees cast a shadow when the Sun is up. The shadow of one tree is 12.1 m long. The shadow of the other tree is 7.6 m long. If the shorter tree is 5.8 m tall, determine the height of the taller tree. Round your answer to the nearest tenth of a metre.</p>
<p>Refer to Question 1. </p><p>a) Find the area of each triangle. </p><p>Question 1</p><p>A right triangle has side lengths 3 cm, 4 cm and 5 cm. </p><p>a) Draw the triangle. </p><p>b) A similar triangle has hypotenuse 30 cm long. What is the scale factor? </p><p>c) What are the lengths of the legs?</p>
<p>Which triangle is congruent to <code class='latex inline'>\triangle ABC</code>?</p><img src="/qimages/995" />
<p>Determine the value of each lower-case letter. If you cannot determine a value, explain why.</p><img src="/qimages/1003" />
<p><strong>i)</strong> For the pair of right triangles, determine whether the triangles are congruent, similar, or neither.</p><p><strong>ii)</strong> If the triangles are congruent, identify the corresponding angles and sides that are equal. If the triangles are similar, identify the corresponding angles that are equal, and calculate the scale factor that relates the smaller triangle as a reduction of the larger triangle.</p><p> <img src="/qimages/998" /></p>
<p>Determine the value of each lower-case letter. If you cannot determine a value, explain why.</p><img src="/qimages/1001" />
<p>Determine the width of this river, if <code class='latex inline'>AB=96</code>m, <code class='latex inline'>AC=204</code>m, and <code class='latex inline'>BD=396</code>m.</p><img src="/qimages/1020" />
<p>The triangles in each pair are similar. Find the unknown side lengths. </p><img src="/qimages/2362" />
<p><code class='latex inline'>\triangle</code>STU<code class='latex inline'>\sim\triangle</code>XYZ. Find the are of <code class='latex inline'>\triangle</code>STU</p><img src="/qimages/2369" />
<p>Which type(s) of triangles will always be similar: right, isosceles, or equilateral?</p>
<p><strong>i)</strong> For the pair of right triangles, determine whether the triangles are congruent, similar, or neither.</p><p><strong>ii)</strong> If the triangles are congruent, identify the corresponding angles and sides that are equal. If the triangles are similar, identify the corresponding angles that are equal, and calculate the scale factor that relates the smaller triangle as a reduction of the larger triangle.</p><p> <img src="/qimages/997" /></p>
<p>An environmental club is designing a logo using triangles, as shown at the right. If the top and bottom lines of the logo at the right are parallel, determine the perimeter of the logo.</p><img src="/qimages/1010" />
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