15. Q15a
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Similar Question 1
<p>Verify that <code class='latex inline'>\triangle ABC</code> is isosceles.</p><img src="/qimages/730" />
Similar Question 2
<p>a) Determine the length of the median from vertex X of <code class='latex inline'>\triangle</code> XYZ. Round your answer to the nearest tenth of a unit.</p><img src="/qimages/22949" /><p>b) Show that <code class='latex inline'>\triangle</code> XYZ is isosceles. </p><p>c) Determine the perimeter of the triangle. Round your answer to the nearest tenth of a unit. </p><p>d) Describe how to use geometry software to answer part c). </p>
Similar Question 3
<p>Determine an equation for the line shown with each triangle.</p><img src="/qimages/728" />
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><code class='latex inline'>P(-7, 1), Q(-8, 4)</code>, and <code class='latex inline'>R(-1, 3)</code> are the vertices of a triangle. Determine if the triangle is scalene, isosceles, or equilateral. </p>
<p>Determine the coordinates of <code class='latex inline'>S</code>, the midpoint of <code class='latex inline'>PR</code>, and <code class='latex inline'>T</code>, the midpoint of <code class='latex inline'>PQ</code> where <code class='latex inline'>P(-12, 6), Q(4, 0)</code>, and <code class='latex inline'>R(-8, -6)</code>.</p>
<p>Construct the bisector of <code class='latex inline'>\angle C</code>, and label the intersection with <code class='latex inline'>\overline{BD}</code> as point Then, bisect <code class='latex inline'>\angle CDE</code>. Continue this process to produce a series of smaller and smaller golden triangles.</p><img src="/qimages/734" />
<p>Use analytic geometry to verify your classification of <code class='latex inline'>\triangle JKL</code> where <code class='latex inline'>J(8, 8), K(-5, -5)</code>, and <code class='latex inline'>L(5, -7)</code></p>
<p>Determine the area of the triangle <code class='latex inline'>\triangle JKL</code> where <code class='latex inline'>J(8, 8), K(-5, -5)</code>, and <code class='latex inline'>L(5, -7)</code></p>
<p>Draw the triangle with vertices <code class='latex inline'>J(8, 8), K(-5, -5)</code>, and <code class='latex inline'>L(5, -7)</code>. What type of triangle does <code class='latex inline'>\triangle JKL</code> appear to be?</p>
<p>Determine an equation for the perpendicular bisector of a line segment with each pair of endpoints.</p><p><code class='latex inline'>C(-2,0)</code> and <code class='latex inline'>D(4,-4)</code></p>
<p><code class='latex inline'>\triangle DEF</code> has vertices at <code class='latex inline'>D(-3, -4), E(-2, -4)</code>, and <code class='latex inline'>F(5, -5)</code>.</p><p>Show that this median is perpendicular to <code class='latex inline'>EF</code> by finding the slopes.</p>
<p>Verify that <code class='latex inline'>\overline{DE}</code> and <code class='latex inline'>\overline{BC}</code> are parallel.</p><img src="/qimages/729" />
<p>Verify that point <code class='latex inline'>C</code> is equidistant from the three vertices of <code class='latex inline'>\triangle DEF</code>.</p><img src="/qimages/5016" />
<p><code class='latex inline'>A(3, 4), B(-2, 0), and C(5, 0)</code>. <code class='latex inline'>D, E</code>, and <code class='latex inline'>F</code> are the midpoints of each side.</p> <ul> <li>Verify that the area of <code class='latex inline'>\triangle ABC</code> is four times the area of <code class='latex inline'>\triangle DEF</code>.</li> </ul>
<p>Find the lengths of the sides of <code class='latex inline'>\triangle DEF</code>.</p><img src="/qimages/731" />
<p>The following points are the vertices of triangles. Determine if the triangle is scalene, isosceles, or equilateral. </p><p><code class='latex inline'>D(2, -3), E(-2, -4), F(6, -6)</code></p>
<p>Verify that the median from vertex B is also an altitude of the triangle.</p><img src="/qimages/730" />
<p>a) Draw <code class='latex inline'>\triangle</code> PQR with vertices P(-5,-4), Q(-3,2), and R(5,1). Then, draw the altitude from vertex Q. </p><p>b) Find an equation for the altitude from vertex Q. </p><p>c) Determine the length of the altitude from vertex Q. </p>
<p>A triangle has vertices <code class='latex inline'>P(a, b), Q(c, d)</code>, and <code class='latex inline'>R(e, f)</code>.</p><p><strong>a)</strong> Determine the coordinates of S and T, the midpoints of <code class='latex inline'>\overline{PQ}</code> and <code class='latex inline'>\overline{PR}</code>, respectively.</p><p><strong>b)</strong> Verify that <code class='latex inline'>ST</code> is parallel to <code class='latex inline'>QR</code></p><p><strong>c)</strong> Verify that <code class='latex inline'>\overline{ST}</code> is half the length of <code class='latex inline'>\overline{QR}</code>.</p>
<p>Verify that the triangle with vertices <code class='latex inline'>I(1, 2), K(-3, -1)</code>, and <code class='latex inline'>L(0, -5)</code> is an isosceles right triangle.</p>
<p>The following points are the vertices of triangles. Determine if the triangle is scalene, isosceles, or equilateral. </p><p><code class='latex inline'>A(3, 3), B(-1, 2), C(0, -2)</code></p>
<p>Draw the triangle with vertices <code class='latex inline'>A(3, 4), B(-2, 0)</code>, and <code class='latex inline'>C(5, 0)</code>. </p> <ul> <li>Find the midpoint of each side, and label these midpoints <code class='latex inline'>D, E</code>, and <code class='latex inline'>F</code>.</li> </ul>
<p>Show that the right bisectors of the sides of <code class='latex inline'>\triangle DEF</code> all intersect at point <code class='latex inline'>C(-4, 4)</code>, the circumcentre of the triangle.</p><img src="/qimages/5016" />
<p>Determine an equation for the line shown with each triangle.</p><img src="/qimages/727" />
<ul> <li>Determine the equations of the right bisectors of the sides of <code class='latex inline'>\triangle OAB</code>.</li> </ul> <img src="/qimages/732" />
<img src="/qimages/610" /><p> Determine an equation for the right bisector of <code class='latex inline'>BC</code>.</p>
<p>Verify that <code class='latex inline'>\overline{DE}</code> = <code class='latex inline'>\overline{BF}</code> by showing that</p> <ul> <li>slope is equal</li> <li>length is equal<br></li> </ul> <img src="/qimages/729" />
<p>a) Show that the triangle with vertices. U(4, 3), V(0, -5), and W(-4, -3) is a right triangle. </p><p>b) Verify that the median from the right angle to the hypotenuse is half as long as the hypotenuse.</p><p>c) Find an equation for the circle that passes through the vertices of <code class='latex inline'>\triangle UVW</code>.</p>
<p>Draw the triangle with vertices<code class='latex inline'> P(-12, 6), Q(4, 0)</code>, and <code class='latex inline'>R(-8, -6)</code>.</p>
<p>What kind of triangle is <code class='latex inline'>\triangle OAB</code>? </p><p>Justify your answer.</p><img src="/qimages/732" />
<p>The vertices of quadrilateral <code class='latex inline'>PQRS</code> are at <code class='latex inline'>P(0, -5), Q(-9, 2), R(-5, 8)</code>, and <code class='latex inline'>S(4, 2)</code>.</p><p>Which of the following show that <code class='latex inline'>PQRS</code> is not a rectangle.</p>
<p><code class='latex inline'>\triangle JKL</code> has vertices at <code class='latex inline'>J(-2,0), K(2,8), </code> and <code class='latex inline'>L(7,3)</code>. Use analytic geometry to determine the coordinates of the circumcentre (the point where the perpendicular bisectors intersect).</p>
<p>How would you find the location that is equal distance to three locations on a map? Describe.</p><img src="/qimages/22178" />
<p>Determine an equation for the line shown with each triangle.</p><img src="/qimages/726" />
<p>a) Plot the triangle with vertices <code class='latex inline'>D(6, 8), E(1, 8)</code>, and <code class='latex inline'>F(4, 2)</code>.</p><p>b) Determine the equation of the right bisector of side DE.</p><p>c) Determine the equation of the right bisector of side EF.</p><p>d) Determine the coordinates of the point</p><p>of The intersection, M, of the right bisectors in parts a) and b).</p><p>e) Show that point M is equidistant from vertices D, E, and F.</p>
<p>A university has three student residences, which are located at points <code class='latex inline'>A(2, 2), 8(10, 6),</code> and <code class='latex inline'>C(4, 8)</code> on grid. The university wants to build tennis court an equal distance from all three residences. Determine the coordinates of the tennis court.</p>
<p>Classify <code class='latex inline'>\triangle DEF</code>. Explain your reasoning.</p><img src="/qimages/731" />
<p>Verify that <code class='latex inline'>\triangle ABC</code> is isosceles.</p><img src="/qimages/730" />
<p><code class='latex inline'>A(3, 4), B(-2, 0)</code>, and <code class='latex inline'>C(5, 0)</code>. <code class='latex inline'>D, E</code>, and <code class='latex inline'>F</code> are the midpoints of each side.</p> <ul> <li>Verify that <code class='latex inline'>\triangle DEF</code> is similar to <code class='latex inline'>\triangle ABC</code>. Find the ratio of the lengths of corresponding sides of these triangles.</li> </ul>
<p>A line, <code class='latex inline'>l_1</code>, has slope <code class='latex inline'>-2</code> and passes through the point <code class='latex inline'>(r, -3)</code>. A second line, <code class='latex inline'>l_2</code>, is perpendicular to <code class='latex inline'>l_1</code>, intersects <code class='latex inline'>l_1</code> at the point <code class='latex inline'>(a, b)</code>, and passes through the point <code class='latex inline'>(6, r)</code>. What is the value of <code class='latex inline'>a</code> in terms of <code class='latex inline'>r</code>.</p>
<p>Decide whether points <code class='latex inline'>P(-2, -3), Q(4, 1)</code>, and <code class='latex inline'>R(2, 4)</code> form a right triangle by showing the length of <code class='latex inline'>\overline{PR}</code> and sum of <code class='latex inline'>|\overline{PR}|^2 +| \overline{QR}|^2</code></p>
<p>Describe all the points that are the same distance from points <code class='latex inline'>A(-3, -1)</code> and <code class='latex inline'>B(5, 3)</code>.</p>
<p>Brandon has three close friends who live in different parts of the city. Brandon wants to meet them for lunch at a restaurant that is roughly equidistant from their homes. How could Brandon use his knowledge of circles to help find a suitable restaurant? Explain your reasoning.</p>
<p>Determine the perimeter of the triangle <code class='latex inline'>\triangle JKL</code> where <code class='latex inline'>J(8, 8), K(-5, -5)</code>, and <code class='latex inline'>L(5, -7)</code></p>
<p>List the other line segments that have equal lengths.</p><img src="/qimages/729" />
<img src="/qimages/610" /><p><strong>i)</strong> Is the equation for the right bisector from <code class='latex inline'>BC</code> same as the median from vertex <code class='latex inline'>A</code>?</p><p><strong>ii)</strong> What property must a triangle have if the median to one of its sides coincides with the right bisector of that side.</p>
<p>The vertices of <code class='latex inline'>\triangle</code> DEF are D(-3, 2), E(l , 4), and F(-l , -6).</p><p>a) Determine the length of the median from D. Round your answer to the nearest tenth.</p><p>b)Determine the length of the median from E. Round your answer to the nearest tenth.</p><p>c) Determine the length of the median of from F.</p>
<p>a) Determine the length of the median from vertex X of <code class='latex inline'>\triangle</code> XYZ. Round your answer to the nearest tenth of a unit.</p><img src="/qimages/22949" /><p>b) Show that <code class='latex inline'>\triangle</code> XYZ is isosceles. </p><p>c) Determine the perimeter of the triangle. Round your answer to the nearest tenth of a unit. </p><p>d) Describe how to use geometry software to answer part c). </p>
<p>Determine whether the point <code class='latex inline'>T(2, -1)</code> lies on the right bisector of the line segment with endpoints <code class='latex inline'>U(3, 5)</code> and <code class='latex inline'>V(-3, -1)</code>. </p><p>Explain your reasoning.</p>
<p>A quadrilateral has vertices at <code class='latex inline'>W(-3, 2), X(2, 4), Y(6, -1)</code>, and <code class='latex inline'>Z(1, -3)</code>.</p> <ul> <li>Determine the difference in the lengths of the two diagonals of WYZ.</li> </ul>
<p>Verify that <code class='latex inline'>\overline{PQ}</code> is twice the length of <code class='latex inline'>\overline{ST}</code>.</p><img src="/qimages/731" />
<p>a) Draw the triangle with vertices <code class='latex inline'>T(-8, 6), U(2, 10)</code>, and <code class='latex inline'>W(4, -4)</code>.</p><p>b) Draw the median from vertex <code class='latex inline'>U</code>. Then, find an equation for this median.</p><p>c) Draw the altitude from vertex <code class='latex inline'>T</code>. Then, find an equation for this altitude.</p><p>d) Draw the right bisector of <code class='latex inline'>TU</code>. Then, find an equation for this right bisector.</p>
<p>The following points are the vertices of triangles. Determine if the triangle is scalene, isosceles, or equilateral.<br> <code class='latex inline'>G(-1, 3), H(-2, -2), I(2, 0)</code></p>
<p>a) Draw a triangle with vertices A (-1, -2), B (7, 3), and C (4, 9). </p><p>b) Determine the coordinates of the midpoints of AB and AC. Label these midpoints D and E. </p><p>c) Show that DE is half the length of BC. </p><p>d) Show that DE is parallel to BC. </p><p>e) Show that the triangle formed by joining the midpoints of the sides of <code class='latex inline'>\triangle</code> ABC is similar to <code class='latex inline'>\triangle</code> ABC.</p>
<p>Draw a smooth curve through points <code class='latex inline'>A, B, C, D</code>, and so on. This curve is a golden spiral.</p><img src="/qimages/734" />
<p>Verify that <code class='latex inline'>ST</code> is half the length of <code class='latex inline'>QR</code> where <code class='latex inline'>P(-12, 6), Q(4, 0)</code>, and <code class='latex inline'>R(-8, -6)</code>.</p>
<p>Verify that the points <code class='latex inline'>A(2, 1), B(8, 5)</code>, and <code class='latex inline'>C(-1, -1)</code> are collinear using</p><p><strong>(a)</strong> slopes</p><p><strong>(b)</strong> an equation of a line</p>
<p>Determine an equation for the right bisector of the line segment with endpoints <code class='latex inline'>P(-5, -2)</code> and <code class='latex inline'>Q(3, 6)</code>.</p>
<p>Find the slopes of the sides of the triangle.</p><img src="/qimages/731" />
<p>Points <code class='latex inline'>P(4, 12), Q(9, 14)</code>, and <code class='latex inline'>R(13, 4)</code> are three vertices of a rectangle.</p><p><strong>a)</strong> Determine the coordinates of the fourth vertex, <code class='latex inline'>5</code>.</p><p><strong>b)</strong> Find the lengths of the diagonal.</p>
<p>a) Show algebraically that this triangle is a right triangle. </p><img src="/qimages/22950" /><p>b) Find the midpoint of the hypotenuse. </p><p>c) Show that this midpoint is equidistant from each of the vertices. </p>
<p>Show that <code class='latex inline'>TU</code>, <code class='latex inline'>T(-1, 7)</code> and <code class='latex inline'>U(3, 5)</code>, is perpendicular to <code class='latex inline'>VW</code>, <code class='latex inline'>V(-4, 1)</code> and <code class='latex inline'>W(-1, 7)</code> by finding the slopes.</p>
<p>Draw a triangle with vertices <code class='latex inline'>P(-3, -4), Q(5, 1)</code>, and <code class='latex inline'>R(2, 7)</code>.</p>
<p>Determine an equation for the line shown with each triangle.</p><img src="/qimages/728" />
<p><code class='latex inline'>\triangle LMN</code> has vertices at <code class='latex inline'>L(O, 4), M(-5, 2)</code>, and <code class='latex inline'>N(2, -2)</code>. Determine the equation of the perpendicular bisector that passes through <code class='latex inline'>MN</code>.</p>
<p>A landscape architect is drawing plans for a rigid triangular canopy to provide shade in a courtyard. On the drawing, the vertices of the canopy are <code class='latex inline'>0(0, 0), P(10, 0)</code>, and <code class='latex inline'>Q(2, 12)</code>. </p><p>A single pole will support the canopy.</p><p><strong>(a)</strong> Verify that the triangular canopy has a centroid.</p><p><strong>(b)</strong> Explain why the centroid is a good location for attaching the canopy to the support pole.</p>
<p>A telecommunication company wants to build a relay tower that is the same distance from two adjacent towns. On a local map, the towns have coordinates <code class='latex inline'>(2, 6)</code> and <code class='latex inline'>(10, 0)</code>.</p><p> Find an equation for this bisector.</p>
<p>A triangle has vertices <code class='latex inline'>L(-7, 0), M(2, 1)</code>, and <code class='latex inline'>N(-3, 5)</code>. Which of the following determine that it is a right isosceles triangle?</p>
<p>Other than <code class='latex inline'>\overline{DE}</code> and <code class='latex inline'>\overline{BC}</code>, list the other line segments that are parallel.</p><img src="/qimages/729" />
<p><code class='latex inline'>A(3, 4), B(-2, 0)</code>, and <code class='latex inline'>C(5, 0)</code>. <code class='latex inline'>D, E</code>, and <code class='latex inline'>F</code> are the midpoints of each side.</p> <ul> <li>How is the ratio of the lengths of corresponding sides related to the ratio of the areas of <code class='latex inline'>\triangle ABC</code> and <code class='latex inline'>\triangle DEF</code>?</li> </ul>
<p>Which of the following Describe the location of the circumcentre of this triangle.</p><img src="/qimages/5015" />
<p>Determine the coordinates of the circumcentre, the point of intersection of the right bisectors of the sides of <code class='latex inline'>\triangle ABC</code> where <code class='latex inline'>A(4, 4), B(8, 0)</code> and <code class='latex inline'>O(0, 0)</code>. </p>
<p>The following points are the vertices of triangles. Determine if the triangle is scalene, isosceles, or equilateral. </p><p><code class='latex inline'>J(2, 5), K(5, -2), L(-1, -2)</code></p>
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