An Introduction to Plane Geometry -- Part 4 by lyxng

steemiteducation · @lyxng · Apr 24 '18 (edited)

$10.47

An Introduction to Plane Geometry -- Part 4

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<center>
<img src=https://steemitimages.com/DQmTz9Z1vRLHpmC27sE1sHrX6VrnFWu6PyWfRtW7YMACu2n/b61c725e11f82db320f304744c235a44.jpg><br>
<sup><i><a href="https://i.pinimg.com/originals/b6/1c/72/b61c725e11f82db320f304744c235a44.jpg">Image Source</a></i></sup>
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<h1>Lesson 4: Plane Geometric Figures</h1>
<p><br></p>
<h3>A. Estimates of plane angle measures</h3>
<p><br></p>
<center>
<img src=https://s19.postimg.cc/if7ls420z/Pics_Art_04-18-05.12.26.jpg><br>
</center>
<p><br></p>
<p><i>The symbol ◻ at vertex P means that ∠BPC measures 90°. If we divide the opening of ∠BPC into three equal parts, as shown below, then m∠SPC=30° ; m∠APS=30° ; and m∠BPA=30°.</i></p>
<center>
<img src=https://s19.postimg.cc/5b21ffhoz/Pics_Art_04-18-06.15.14.jpg><br>
</center>
<p><i>Ray PM divides ∠BPC into two congruent measures, therefore m∠BPM=45° and m∠MPC=45°.</i></p>
<center>
<img src=https://s19.postimg.cc/ce9wv5aar/Pics_Art_04-18-06.33.09.jpg><br>
</center>
<p><br></p>
<p>Let us extend line PC to the left and locate point X on it.</p>
<center>
<img src=https://s19.postimg.cc/orvxtgmfn/Pics_Art_04-18-06.49.24.jpg><br>
</center>
<ul>
 <li><i>What is the measure of ∠BPX? Why?</i></li>
 <li><i>Can you estimate and illustrate 30°, 45°, 60°, 90° and 120° using parts of your body?</i></li>
</ul>
<p><br></p>
<p><b>Given:</b> Line PY is inclined at 30° with the horizontal. Line BX is perpendicular to line PY at point A.</p>
<center>
<b>(BX ⊥ PY at A)</b><br>
<img src=https://s19.postimg.cc/yq7pojh4j/Pics_Art_04-18-07.17.25.jpg><br>
</center>
<p><b>Complete the statements below:</b></p>
<p>1. &nbsp;m∠BAY = _________ . Why?</p>
<p>2. &nbsp;m∠2 + m∠3 + m∠4 = __________ . Why?</p>
<p>3. &nbsp;∠1 ≅ __________ . Why?</p>
<p><br></p>
<h3>B. Polygons</h3>
<p><br></p>
<blockquote><i>A polygon is a closed plane figure bounded by line segments.</i></blockquote>
<blockquote><i>The distance around any polygon is called its perimeter.</i></blockquote>
<p><br></p>
<p>Which of the following figures below are not polygons? Why?</p>
<center>
<img src=https://s19.postimg.cc/j4qe4lklv/Pics_Art_04-18-08.00.59.jpg><br>
</center>
<p><i>A regular polygon is a polygon with congruent sides.</i></p>
<p><br></p>
<h3>Kinds of polygons according to the number of their sides:</h3>
<p>&nbsp;1. &nbsp;Triangle, a three-sided polygon</p>
<p>&nbsp;2. &nbsp;Quadrilateral, a four-sided polygon</p>
<p>&nbsp;3. &nbsp;Pentagon, a five-sided polygon</p>
<p>&nbsp;4. &nbsp;Hexagon, a six-sided polygon</p>
<p>&nbsp;5. &nbsp;Heptagon, a seven-sided polygon</p>
<p>&nbsp;6. &nbsp;Octagon, an eight-sided polygon</p>
<p>&nbsp;7. &nbsp;Nonagon, a nine-sided polygon</p>
<p>&nbsp;8. &nbsp;Decagon, a ten-sided polygon</p>
<p>&nbsp;9. &nbsp;Undecagon, an eleven-sided polygon</p>
<p>10. Dodecagon, a twelve-sided polygon</p>
<p><br></p>
<h3>A. Triangles</h3>
<p><br></p>
<ul>
 <li><i>A triangle is formed when three noncollinear points are joined by line segments.</i></li>
 <li><i>The sum of the three interior angles of a triangle is 180°.</i></li>
 <li><i>The total exterior angles of a triangle and all other polygons is 360°.</i></li>
 <li><i>A triangle is named by its three vertices like triangle ABC or ∆ABC.</i></li>
</ul>
<p><br></p>
<div class=pull-left><img src=https://s19.postimg.cc/vw4kb4hj7/Pics_Art_04-18-08.06.38.jpg></div><div class=pull-right><br>∆ABC, ∆BAC<br>∆BCA, ∆ACB<br>∆CAB, ∆CBA<br></div>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<h3>Kinds of triangles according to their sides;</h3>
<p>&nbsp;1. &nbsp;Equilateral Triangle</p>
<blockquote><i>An equilateral triangle is a triangle with three sides congruent.</i></blockquote>
<div class=pull-left><img src=https://s19.postimg.cc/8hwkz77bn/Pics_Art_04-18-08.08.49.jpg></div><div class=pull-right>AB ≅ BC ≅ AC<br>If line segment AB is 5cm, then BC=5cm and AC=5cm</div>
<p><br></p>
<br><br><br><br><br>
<p>Equilateral triangles are also equiangular, which means that m∠A = m∠B = m∠C.</p>
<p><br></p>
<p>&nbsp;2. &nbsp;Isosceles Triangle</p>
<blockquote><i>An isosceles triangle is a triangle with two congruent sides.</i></blockquote>
<div class=pull-left><img src=https://s19.postimg.cc/8556t14hf/Pics_Art_04-18-08.15.19.jpg></div><div class=pull-right><ul>
 <li>If ∆MNO is isosceles, then line segment MN is congruent to line segment NO. (MN ≅ NO).</li>
 <li>MO is the base.</li>
 <li>∠M and ∠O are the base angles.</li>
 <li>∠M ≅ ∠O.</li>
</ul></div>
<br><br><br><br><br><br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<p><i>Base angles of isosceles triangles are congruent.</i></p>
<p><br></p>
<p>&nbsp;3. &nbsp;Scalene Triangle</p>
<blockquote><i>A scalene triangle is a triangle with no sides congruent.</i></blockquote>
<center>
<img src=https://s19.postimg.cc/d3sp7knpv/Pics_Art_04-18-08.19.22.jpg>
</center>
<p><i>∆RST is a scalene triangle.</i></p>
<p><br></p>
<p><b>Answer the following:</b></p>
<p>&nbsp;1. A side of an equilateral triangle is 20 centimeters. What is the length of its perimeter?</p>
<p>&nbsp;2. The upper vertex angle of an isosceles triangle measures 80°. What is the measure of a base angle?</p>
<p>&nbsp;3. If ∆PXY is equiangular, what is the measure of ∠P?</p>
<p><br></p>
<h3>Previous Lessons</h3>
<ul>
 <li><a href="https://steemit.com/steemiteducation/@lyxng/an-introduction-to-plane-geometry-part-1"><b>An Introduction to Plane Geometry -- Part 1</b></a></li>
 <li><a href="https://steemit.com/steemiteducation/@lyxng/an-introduction-to-plane-geometry-part-2"><b>An Introduction to Plane Geometry -- Part 2</b></a></li>
 <li><a href="https://steemit.com/steemiteducation/@lyxng/an-introduction-to-plane-geometry-part-3"><b>An Introduction to Plane Geometry -- Part 3</b></a></li>
</ul>
<p><br></p>
<center>
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