18. Q18a
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Similar Question 1
<p>Here are the first three stages of a Koch snowflake, named after Swedish mathematician Niels Fabian Helge von Koch (1870 - 1924). This snowflake starts with an equilateral triangle. At each state, the middle third of each side is replaced by two segments, each equal in length to the segment they replace.</p><img src="/qimages/617" /><p>Find the coordinates of the three new vertices on the bottom of the snowflake in the second stage.</p>
Similar Question 2
<p><code class='latex inline'>A</code> is the midpoint of <code class='latex inline'>BC, D</code> is the midpoint of <code class='latex inline'>AC</code>, and <code class='latex inline'>E</code> is the midpoint of <code class='latex inline'>AD</code>. <code class='latex inline'>ED</code> is 2 units in length. What is the length of <code class='latex inline'>BC</code>?</p>
Similar Question 3
<p><code class='latex inline'>A</code> is the midpoint of <code class='latex inline'>BC, D</code> is the midpoint of <code class='latex inline'>AC</code>, and <code class='latex inline'>E</code> is the midpoint of <code class='latex inline'>AD</code>. <code class='latex inline'>ED</code> is 2 units in length. What is the length of <code class='latex inline'>BC</code>?</p>
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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><strong>(a)</strong> Draw <code class='latex inline'>\triangle PQR</code> with vertices <code class='latex inline'>P(0, 0), Q(16, 0)</code>, and <code class='latex inline'>R(0, 16)</code>.</p><p><strong>(b)</strong> Construct the midpoints of <code class='latex inline'>PQ</code>. <code class='latex inline'>QR</code>, and <code class='latex inline'>PR</code>, and label them <code class='latex inline'>S, T</code> and <code class='latex inline'>U</code> respectively.</p><p><strong>(c)</strong> Join the midpoints to form <code class='latex inline'>\triangle STU</code>. The length of a line segment joining the midpoints of two sides of a triangle is half the length of the third side. Use this property to show that <code class='latex inline'>\triangle STU</code> is congruent to all three of the other triangles inside <code class='latex inline'>\triangle PQR</code>.</p><p><strong>(d)</strong> Compare the area of <code class='latex inline'>\triangle STU</code> to the area of <code class='latex inline'>\triangle PQR</code>.</p><p><strong>(e)</strong> Shade <code class='latex inline'>\triangle STU</code>. Construct and label the midpoint of each side of the three other triangles inside <code class='latex inline'>\triangle PQR</code>. Join the midpoints to create a set of even smaller triangles.</p><p><strong>(f)</strong> Compare the area of one of these triangles to the area of <code class='latex inline'>\triangle STU</code> and to the area of <code class='latex inline'>\triangle PQR</code>.</p>
<p><code class='latex inline'>A</code> is the midpoint of <code class='latex inline'>BC, D</code> is the midpoint of <code class='latex inline'>AC</code>, and <code class='latex inline'>E</code> is the midpoint of <code class='latex inline'>AD</code>. <code class='latex inline'>ED</code> is 2 units in length. What is the length of <code class='latex inline'>BC</code>?</p>
<p>Here are the first three stages of a Koch snowflake, named after Swedish mathematician Niels Fabian Helge von Koch (1870 - 1924). This snowflake starts with an equilateral triangle. At each state, the middle third of each side is replaced by two segments, each equal in length to the segment they replace.</p><img src="/qimages/617" /><p>Find the coordinates of the three new vertices on the bottom of the snowflake in the second stage.</p>
<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>P(0, 2)</code> is the midpoint of side <code class='latex inline'>AB</code>, <code class='latex inline'>Q(2, 4)</code> is the midpoint of <code class='latex inline'>BC</code>, and <code class='latex inline'>R(1, 0)</code> is the midpoint of <code class='latex inline'>AC</code>.</p><p>Find the coordinates of <code class='latex inline'>A, B</code>, and <code class='latex inline'>C</code>. (Hint: Use the properties of a line segment joining the midpoints of two sides of a triangle.)</p>
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