20. Q20
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Similar Question 1
<p>Use the dimensions of the surveyors&#39; triangles to find the width of the river, to the nearest metre.</p><img src="/qimages/5610" />
Similar Question 2
<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>
Similar Question 3
<p>The areas of two similar triangle are <code class='latex inline'>72 cm^2</code> and <code class='latex inline'>162 cm^2</code>. What is the ratio of the lengths of their corresponding sides?</p>
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
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<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/65150" />
<p>Find the length and width of the oval. The following measures are known:</p><p><code class='latex inline'>AB = 14 m, BC = 11m</code></p><p>Assume that XY is a line of symmetry for the pond.</p><img src="/qimages/5612" />
<p><code class='latex inline'> \triangle \mathrm{ABC} </code> and <code class='latex inline'> \triangle \mathrm{DEF} </code> are similar. The ratio of thein corresponding sides is <code class='latex inline'> 3: 5 . </code> What is the ratio of their perimeters? Explain.</p>
<p>The areas of two similar triangle are <code class='latex inline'>72 cm^2</code> and <code class='latex inline'>162 cm^2</code>. What is the ratio of the lengths of their corresponding sides?</p>
<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>The pairs of triangles are similar. Find the unknown side lengths.</p><img src="/qimages/5465" />
<p> <code class='latex inline'> \triangle \mathrm{PQR} </code> and <code class='latex inline'> \triangle \mathrm{LMN} </code> are similar. Can they be congruent? Explain and justify your answer.</p>
<p>For each pair of similar triangles find all the missing measures.</p><p><code class='latex inline'>\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{BDE} </code></p><img src="/qimages/156338" />
<p>Find x.</p><img src="/qimages/65153" />
<p> <code class='latex inline'> \triangle \mathrm{PQR} </code> and <code class='latex inline'> \triangle \mathrm{LMN} </code> are congruent. Are they similar? Explain and justify your answer.</p>
<p>In a roof, a 1.5-m support is to be placed at point B, as shown. Find the length of the support to be placed at point A, to the nearest tenth of a metre.</p><img src="/qimages/9470" />
<p>For <code class='latex inline'>\triangle ABC \sim \triangle DEF</code>:</p><p>a) Determine the length of <code class='latex inline'>BC</code></p><p>b) Determine the length of <code class='latex inline'>DE</code></p><p>c) Is <code class='latex inline'>\triangle GHI \sim \triangle DEF</code>? Explain.</p><img src="/qimages/7278" />
<p>Name a pair of similar triangles in each diagram and explain why they are similar.</p><img src="/qimages/1130" />
<p><code class='latex inline'>\triangle DEF</code> ~ <code class='latex inline'>\triangle ABC</code>. Find the area of <code class='latex inline'>\triangle DEF</code>.</p><img src="/qimages/22835" />
<p> To find the height of a tree, Sarah placed a mirror on the ground <code class='latex inline'> 15 \mathrm{~m} </code> from the base of the tree. She walked backward until she could see the top of the tree in the centre of the mirror. At that position she was <code class='latex inline'> 1.2 \mathrm{~m} </code> from the mirror and her eyes were <code class='latex inline'> 1.4 \mathrm{~m} </code> from the ground. Find the height of the tree. <code class='latex inline'> 1.4 \mathrm{~m} </code> </p><img src="/qimages/65167" />
<p>For each pair of similar triangles find all the missing measures.</p><p><code class='latex inline'>\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} </code></p><img src="/qimages/156340" />
<p>For each pair of similar triangles:</p><p>List the corresponding angles.</p><p>List the corresponding sides.</p><p>List the ratios of the corresponding sides.</p><p>Write the proportionality statement for the corresponding sides.</p><p><code class='latex inline'>\displaystyle \triangle \mathrm{PQR} \sim \triangle \mathrm{STU} </code></p><img src="/qimages/156332" />
<p>The areas of two similar triangles are <code class='latex inline'> 72 \mathrm{~cm}^{2} </code> and <code class='latex inline'> 162 \mathrm{~cm}^{2} </code> . What is the ratio of the lengths of their corresponding sides?</p>
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/22831" />
<p>Use algebraic and geometric reasoning to show how the areas of two similar right triangle are relate by the square of the scale factor, <code class='latex inline'>k^2</code>.</p>
<p><code class='latex inline'>\triangle MNO</code> ~ <code class='latex inline'>\triangle JKL</code>. Find the area of <code class='latex inline'>\triangle MNO</code>.</p><img src="/qimages/22837" />
<p>Find the length of the indicated side to the nearest tenth of a unit.</p><p>Find the length of <code class='latex inline'>\displaystyle x </code>.</p><img src="/qimages/156343" />
<p><code class='latex inline'>\triangle</code> ABC ~ <code class='latex inline'>\triangle</code> RST. Complete each statement.</p><p>a) <code class='latex inline'>\angle ABC</code> = <code class='latex inline'>\blacksquare</code></p><p>b) <code class='latex inline'>\angle BCA = \blacksquare</code></p><p>c) <code class='latex inline'>\frac{AB}{RS} = \blacksquare</code></p><p>d) <code class='latex inline'>\triangle STR \sim \blacksquare </code></p><p>e) <code class='latex inline'>\frac{ST}{BC} = \blacksquare</code></p><p>f) <code class='latex inline'>\angle SRT = \blacksquare</code></p>
<p>Name the two similar triangles and explain why they are similar.</p><img src="/qimages/9457" />
<p>Find x .</p><img src="/qimages/65152" />
<p>Are all equilateral triangles similar? Justify your answer.</p>
<p><code class='latex inline'>\triangle GHI</code> ~ <code class='latex inline'>\triangle STU</code>. Find the area of <code class='latex inline'>\triangle GHI</code>.</p><img src="/qimages/22838" />
<p>a) Show why <code class='latex inline'>\triangle ABC</code> is similar to <code class='latex inline'>\triangle DEC</code>.</p><p>b) Find the lengths <code class='latex inline'>x</code> and <code class='latex inline'>y</code>.</p><img src="/qimages/22828" />
<p>Given <code class='latex inline'>\displaystyle \triangle \mathrm{DEF} \sim \triangle \mathrm{RPQ}, \mathrm{EF}=10 </code> in., <code class='latex inline'>\displaystyle \mathrm{DF}=9 </code> in., <code class='latex inline'>\displaystyle \mathrm{DE}=8 \mathrm{in} </code> and <code class='latex inline'>\displaystyle \mathrm{RQ}=0.5 \mathrm{ft} </code>. Find the length of side <code class='latex inline'>\displaystyle \mathrm{PQ} </code>.</p><p>Given <code class='latex inline'>\displaystyle \triangle \mathrm{DEF} \sim \triangle \mathrm{RPQ}, \mathrm{EF}=10 </code> in., <code class='latex inline'>\displaystyle \mathrm{DF}=9 </code> in., <code class='latex inline'>\displaystyle \mathrm{DE}=8 \mathrm{in} </code> and <code class='latex inline'>\displaystyle \mathrm{RQ}=0.5 \mathrm{ft} </code>. Find the length of side <code class='latex inline'>\displaystyle \mathrm{PQ} </code>.</p>
<p><code class='latex inline'>\triangle ABC</code> and <code class='latex inline'>\triangle DEF</code> are similar. The ratio of their corresponding sides is 3:5. What is the ratio of their perimeters? Explain.</p>
<p>Determine the value of <code class='latex inline'>x</code> and <code class='latex inline'>y</code>.</p><img src="/qimages/7277" />
<p>Triangles <code class='latex inline'>\displaystyle \mathrm{ABC} </code> and <code class='latex inline'>\displaystyle \mathrm{XYZ} </code> are similar. Angles <code class='latex inline'>\displaystyle \mathrm{A} </code> and <code class='latex inline'>\displaystyle \mathrm{C} </code> are equal, <code class='latex inline'>\displaystyle \mathrm{XZ} </code> is <code class='latex inline'>\displaystyle 21 \mathrm{~cm} </code> long, <code class='latex inline'>\displaystyle \mathrm{AB} </code> is <code class='latex inline'>\displaystyle 7 \mathrm{~cm} </code> long, and <code class='latex inline'>\displaystyle \mathrm{AC} </code> is <code class='latex inline'>\displaystyle 35 \mathrm{~cm} </code> long.</p><p>a) Find the length of YZ.</p><p>b) Compare your answer to part a) with that of a classmate. Did you get the same answer? If your answers are different, work together to find which answer, if either, is correct.</p><p>Triangles <code class='latex inline'>\displaystyle \mathrm{ABC} </code> and <code class='latex inline'>\displaystyle \mathrm{XYZ} </code> are similar. Angles <code class='latex inline'>\displaystyle \mathrm{A} </code> and <code class='latex inline'>\displaystyle \mathrm{C} </code> are equal, <code class='latex inline'>\displaystyle \mathrm{XZ} </code> is <code class='latex inline'>\displaystyle 21 \mathrm{~cm} </code> long, <code class='latex inline'>\displaystyle \mathrm{AB} </code> is <code class='latex inline'>\displaystyle 7 \mathrm{~cm} </code> long, and <code class='latex inline'>\displaystyle \mathrm{AC} </code> is <code class='latex inline'>\displaystyle 35 \mathrm{~cm} </code> long.</p><p>a) Find the length of YZ.</p><p>b) Compare your answer to part a) with that of a classmate. Did you get the same answer? If your answers are different, work together to find which answer, if either, is correct.</p>
<p>For each pair of similar triangles find all the missing measures.</p><p><code class='latex inline'>\displaystyle \triangle \mathrm{DEF} \sim \triangle \mathrm{XYZ} </code></p><img src="/qimages/156335" /><img src="/qimages/156336" />
<p>The scale on a map is 1 cm represents 5 km. A provincial park has an area of <code class='latex inline'>6 cm^2</code> on the map. What is the actual area of the park, to the nearest square kilometre?</p>
<p>The pairs of triangles are similar. Find the unknown side lengths.</p><img src="/qimages/5466" />
<p>A right triangle has side lengths 6 cm, 8 cm, and 10 cm. The longest side of a larger similar triangle measures 15 cm. Determine the perimeter and area of the larger triangle.</p>
<img src="/qimages/5614" /><p>a) Calculate the length of <code class='latex inline'>ZX</code> and the measure of <code class='latex inline'>\angle ZXY</code>.</p><p>b) If the hypotenuse of the actual flower garden measures 6.5 m, what is the perimeter of the actual garden?</p><p>c) What is the scale factor of the drawing?</p><p>d) What is the ratio of the area of the flower garden to the area of the scale drawing?</p>
<p>While looking through a cylindrical tube, Rachel moves to a point where the height of a picture just fits within her field of view, as shown. </p><img src="/qimages/5613" /><p>Rachael is standing 1.5 m from the picture. The length and diameter of the viewing tube are as shown. Find the height of the picture.</p>
<p>Use the dimensions of the surveyors&#39; triangles to find the width of the river, to the nearest metre.</p><img src="/qimages/5610" />
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/65143" />
<p>Given <code class='latex inline'>\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}, a=2.1 \mathrm{~cm}, c=5.8 \mathrm{~cm}, e=8.7 \mathrm{~cm} </code>, and <code class='latex inline'>\displaystyle f=6.9 \mathrm{~cm} </code>. Work with a partner. Discuss how you would find the length of <code class='latex inline'>\displaystyle d </code> and <code class='latex inline'>\displaystyle b </code>. Find the lengths of <code class='latex inline'>\displaystyle d </code> and <code class='latex inline'>\displaystyle b </code> to the nearest tenth of a centimetre.</p><img src="/qimages/156349" />
<p>Nora, who is 172.0 cm tall, is standing near a tree. Nora’s shadow is 3.2 m long. At the same time, the shadow of the tree is 27.0 m long. How tall is the tree?</p>
<p>Given that two triangles <code class='latex inline'>\displaystyle \mathrm{ABC} </code> and <code class='latex inline'>\displaystyle \mathrm{PQR} </code> are similar and that <code class='latex inline'>\displaystyle \angle \mathrm{A}=50^{\circ}, \angle \mathrm{B}=90^{\circ}, \mathrm{PQ}=12 \mathrm{~cm}, \mathrm{AB}=4 \mathrm{~cm} </code>, and <code class='latex inline'>\displaystyle \mathrm{BC}=5 \mathrm{~cm} </code> find the measures of all the missing sides and angles.</p><p>Given that two triangles <code class='latex inline'>\displaystyle \mathrm{ABC} </code> and <code class='latex inline'>\displaystyle \mathrm{PQR} </code> are similar and that <code class='latex inline'>\displaystyle \angle \mathrm{A}=50^{\circ}, \angle \mathrm{B}=90^{\circ}, \mathrm{PQ}=12 \mathrm{~cm}, \mathrm{AB}=4 \mathrm{~cm} </code>, and <code class='latex inline'>\displaystyle \mathrm{BC}=5 \mathrm{~cm} </code> find the measures of all the missing sides and angles.</p>
<p>Identify the two similar triangles and explain why they are similar.</p><img src="/qimages/9423" />
<p>Cam is designing a new flag for his hockey team. The flag will be triangular, with sides that measure 0.8 m, 1.2 m, and 1.0 m. Cam has created a scale diagram, with sides that measure 20 cm, 30 cm, and 25 cm, to take to a flag maker. Did Cam create his scale diagram correctly?</p>
<p>Find the length of x, to the nearest centimetre.</p><img src="/qimages/9432" />
<p>Name the two similar triangles and explain why they are similar.</p><img src="/qimages/5464" />
<p>The pairs of triangles are similar. Find the unknown side lengths.</p><img src="/qimages/5467" />
<p><code class='latex inline'>\triangle XYZ</code> ~ <code class='latex inline'>\triangle PQR</code>. Find the area of <code class='latex inline'>\triangle XYZ</code>.</p><img src="/qimages/22836" />
<p>Find the length of <code class='latex inline'>x</code> in each.</p><img src="/qimages/22834" />
<p>The tips of the shadows of a tree and of a metre stick meet at the point <code class='latex inline'>X</code>.</p><img src="/qimages/5468" /><p>The following measurements are taken: </p><p><code class='latex inline'>XS = 3.5 m</code></p><p><code class='latex inline'>ES = 6.5 m</code></p><p>Use this information to find the height of the tree, to the nearest tenth of a metre.</p>
<p> A <code class='latex inline'> 5-m </code> flagpole casts a <code class='latex inline'> 4-m </code> shadow at the same time of day as a building casts a <code class='latex inline'> 30-\mathrm{m} </code> shadow. How tall is the building?</p><img src="/qimages/65160" />
<p>Find the length of the indicated side to the nearest tenth of a unit.</p><p> Find the length of side DE.</p><img src="/qimages/156342" />
<p>Connie placed a mirror on the ground, 5.00 m from the base of a flagpole. She stepped back until she could see the top of the flagpole reflected in the mirror. Connie’s eyes are 1.50 m above the ground and she saw the reflection when she was 1.25 m from the mirror. How tall is the flagpole?</p>
<p>State whether the triangles in the diagram are similar. Then determine p.</p><img src="/qimages/9923" />
<p>A right triangle has side lengths 7 cm, 24 cm, and 25 cm.</p><p>a) Draw the triangle.</p><p>b) A similar triangle has a hypotenuse 75 cm long. What is the scale factor?</p><p>c) What are the lengths of the legs?</p><p>d) Draw the similar triangle.</p>
<p>In <code class='latex inline'>\displaystyle \triangle \mathrm{VWX}, \mathrm{WX}=28 \mathrm{~cm}, \mathrm{VX}=35 \mathrm{~cm} </code>, and <code class='latex inline'>\displaystyle \mathrm{VW}=14 \mathrm{~cm} . </code> In <code class='latex inline'>\displaystyle \triangle \mathrm{PQR}, \mathrm{QR}=20 \mathrm{~cm}, \mathrm{PR}=25 \mathrm{~cm} </code>, and <code class='latex inline'>\displaystyle \mathrm{PQ}=10 \mathrm{~cm} </code>. Are triangles VWX and PQR similar? How do you know?</p>
<p>Use the given measures to find the width of the pond, to the nearest tenth of a metre.</p><img src="/qimages/22839" />
<p>In the diagram, DE is parallel to <code class='latex inline'>\displaystyle \mathrm{AC} . \mathrm{BD}=4, \mathrm{DA}=6 </code>, and <code class='latex inline'>\displaystyle \mathrm{BE}=5 . </code> Find the length of <code class='latex inline'>\displaystyle \mathrm{BC} </code> to the nearest tenth of a unit.</p><img src="/qimages/156347" />
<p> Are all isosceles triangles similar? Are some isosceles triangles similar? Explain, using diagrams where necessary, and justify your reasoning.</p>
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/22830" />
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/65144" />
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/65149" />
<p>Name the triangles that are</p><p>a) congruent to <code class='latex inline'>\triangle</code> ABC</p><p>b) similar to <code class='latex inline'>\triangle</code> ABC</p><img src="/qimages/156254" />
<p> Are all equilateral triangles similar? Explain and justify your reasoning.</p>
<img src="/qimages/8520" /><p>Jim has a triangular shelf system that attaches to his showerhead. </p><p>The total height of the system is 18 inches, and there are three parallel shelves as shown above. </p><p>What is the maximum height, in inches, of a shampoo bottle that can stand upright on the middle shelf?</p>
<p>In <code class='latex inline'>\triangle ABC, AB= 24 cm</code> and <code class='latex inline'>BC = 10 cm</code>. <code class='latex inline'>BD</code> is perpendicular to <code class='latex inline'>AC</code>. Find the ratio of the shaded area to the unshaded area.</p><img src="/qimages/5616" />
<p>For each pair of similar triangles, write the equivalent ratios of side lengths.</p><img src="/qimages/1129" />
<p>Write a proportion for the corresponding side lengths in these similar triangles.</p><img src="/qimages/7276" />
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/65148" />
<p>Are all isosceles triangles similar? Justify your answer.</p>
<p>Given that <code class='latex inline'>\displaystyle \mathrm{DE} </code> is parallel to <code class='latex inline'>\displaystyle \mathrm{AC}, \mathrm{AD}=6.8, \mathrm{DB}=9.3 </code> and <code class='latex inline'>\displaystyle \mathrm{BC}=12.8 </code>, find the length of <code class='latex inline'>\displaystyle \mathrm{BE} </code> to the nearest tenth of a unit.</p><img src="/qimages/156345" />
<p>Billy has lost track of time. He will get in trouble if he is late for dinner. but he will get in more trouble if he comes home with wet shoes. Racing home, Billy suddenly encounters a creek, as shown. Glancing at some nearby rocks. he estimates the distances indicated.</p><img src="/qimages/9398" /><p>Billy can long jump about 2 m. Should he try to jump the creek, or take the long way home across the wooden bridge? Justify your reasoning.</p>
<p>A crest for hockey team looks like the diagram below. The shape consists of four congruent equilateral triangles.</p><img src="/qimages/5611" /><p>a) What is the total area of this crest?</p><p>b) What is the area of </p> <ul> <li>the green section?</li> <li>the purple sections?</li> </ul> <p>c) What is the area of a giant similar crest with base 30 cm?</p><p>d) What is the height of a similar crest with area <code class='latex inline'>500 cm^2</code> ?</p>
<p>Name the two similar triangles and explain why they are similar.</p><img src="/qimages/5463" />
<img src="/qimages/65154" /><img src="/qimages/65156" />
<p>Surveyors have laid out triangles to find the length of a lake. Calculate this length, <code class='latex inline'> \mathrm{AB} </code> .</p><img src="/qimages/65162" />
<p>a) Show why <code class='latex inline'> \triangle P Q R </code> 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/65158" />
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/22832" />
<p>To measure the height of a garage, Brian has his brother Victor stand so that the tip of his shadow coincides with the tip of the building&#39;s shadow at point A.</p><img src="/qimages/22840" /><p>Brian&#39;s brother, who is 1.4 m tall, is 3.4 m from Brian, who is standing at A, and 7.6 m from the base of the building. Find the height of the building, <code class='latex inline'>DE</code>, to the nearest tenth of a metre.</p>
<p>Carol is building a staircase from the floor of her barn to the loft, which is 3.6 m above the floor. She is using steps that are each 30 cm high and 40 cm deep.</p><img src="/qimages/5615" /><p>a) How much floor clearance will Carol need in order to fit the staircase?</p><p>b) How many steps will be required?</p>
<p>The figures in each pair are similar. Find the value of <code class='latex inline'>\displaystyle x </code>.</p><img src="/qimages/60794" />
<p>The triangles in each pair are similar. Find the unknown side lengths.</p><img src="/qimages/22829" />
<p>Name the similar triangle in each case. Write the letters so that equal angles appear in corresponding order.</p><img src="/qimages/1129" />
<p>Name a pair of similar triangles in each diagram and explain why they are similar.</p><img src="/qimages/1131" />
<p>Find the length of <code class='latex inline'>x</code> in each.</p><img src="/qimages/22833" />
<p>The figures in each pair are similar. Find the value of <code class='latex inline'>\displaystyle x </code>.</p><img src="/qimages/60795" />
<p>The figures in each pair are similar. Find the value of <code class='latex inline'>\displaystyle x </code>.</p><img src="/qimages/60796" />
<p>The neighbouring houses are located at <code class='latex inline'>A</code> and <code class='latex inline'>B</code>, near a straight section of a rural road, RD. The electric company plans to place a pole, <code class='latex inline'>P</code>, at the roadside and connect wires from the pole to the two houses. How far from point R should the pole be located so that the minimum length of wire is needed?</p><img src="/qimages/5617" />
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