Theorems & Definitions for Chpt. 4

StudyBlue printing of Theorems & Definitions for Chpt. 4 html, body, div, span, applet, object, iframe, h1, h2, h3, h4, h5, h6, p, blockquote, pre, a, abbr, acronym, address, big, cite, code, del, dfn, em, font, img, ins, kbd, q, s, samp, small, strike, strong, sub, sup, tt, var, b, u, i, center, fieldset, form, label, legend, table, caption, tbody, tfoot, thead, tr, th, td { margin: 0; padding: 0; border: 0; outline: 0; font-size: 100%; background: transparent; } body { line-height: 1; } blockquote, q { quotes: none; } blockquote:before, blockquote:after, q:before, q:after { content: ''; content: none; } /* remember to define focus styles! */ :focus { outline: 0; } /* remember to highlight inserts somehow! */ ins { text-decoration: none; } del { text-decoration: line-through; } /* tables still need 'cellspacing="0"' in the markup */ table { border-collapse: collapse; border-spacing: 0; } /* end RESET */ .header { min-width:800px; } .logo { padding:6px 20px 2px 20px; margin:0; font-size:25px; font-weight:bold; color:#808285; position:relative; border-bottom: 1px solid #c5c5c5; } .logo-blue { color:#70adc4; } .logo-desc { font-weight:normal; font-size:19px; color:#cccccc; margin-top:50px; position:absolute; display: none; } .back-button { position:absolute; top:20px; right:20px; font-size:13px; line-height:25px; color:rgb(0,175,225); font-weight:normal; } .back-button a { color:rgb(0,175,225); } .instructions { padding:0; margin:0; width:100%; position:relative; color:rgb(100,100,100); } .step-holder { border-left:1px solid #ededed; margin-left:20px; } .steps { padding:15px 0; float:left; width:24%; border-right:1px solid #ededed; text-align:center; } .steps-01 { } .steps-02 { } .steps-03 { } .steps-04 { } .label { padding:5px 10px; } .print-button { } .print-button a { background-color:rgb(0,175,225); color:white; line-height: 19px; padding:9px 8px 5px 30px; font-size:14px; text-decoration:none; background-image: url(images/printer.png); background-repeat: no-repeat; background-position: 7px 50%; -moz-border-radius: 5px; -webkit-border-radius: 5px; } .print-button a:hover { background-color:black; } .theNote .content { width: 8.0in !important; margin: 5px auto; padding:20px; background-color:white; } .theNote .header { border-bottom: 1px dashed #C8C8C8; font-size: 17px; padding: 0 0 10px; line-height: 19px; color: #00ADE1; min-width:500px; } .theNote .body { font-size: 14px; line-height: 19px; padding: 10px 0; } .theNote{ padding:6px 0; clear:both; background-color: rgb(200,200,200); } .theNote h3{ color: rgb(100,100,100); } .theNote h1, .theNote h3{ background-color:white; padding:2px 20px; width:8.0in !important; margin: 0 auto; font-size: 15px; } .theNote h1{ padding-top: 10px; font-size: 15px; } .theNote h1:first-child{ font-size: 20px; } .theNote h3 { font-size: 14px; font-weight: normal; } #options { border: 3px double #ccc; padding: 5px 12px; margin: 10px 50px 10px 20px; float: left; } #info { border-top: 1px solid #ccc; padding-top: 5px; font-style: italic; } li { margin: 5px 10px 5px 25px; } ul li { list-style: disc; } ol li { list-style: decimal; } img { border: 0; } table { clear: both; width: 100%; border: 1px solid #c5c5c5; border-width: 1px 0; margin: 0; page-break-after: always; } table#page { page-break-after: auto; } td { text-align: center; font-size: 12px; border-bottom: 1px dashed #c5c5c5; height: 1.75in; width: 50%; padding-left: 15px; } .leftside { border-right: 1px solid #cccccc; padding: 0 15px 0 0; } .bottom td { border-bottom: none; } .clearfix { clear:both; line-height:1px; height:1px; } img { max-width:80%; max-height:150px; margin:20px; } @media print {.header { display: none; } .content .header{ display:inherit; } table { border: 1px dashed #bbb; border-width: 1px 0; } .theNote{ background-color:white; } } Theorems & Definitions for Chpt. 4 Theorem 4-1 Opposite sides of a parallelogram are congruent. Corollary for Theorem 4-1 If two lines are parallel, then all the points on one line are equidistant from the other line. Theorem 4-2 Opposite angles of a parallelogram are congruent. Theorem 4-3 The Diagonals of a parallelogram bisect each other Theorem 4-4 If bother pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 4-5 If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram. Theorem 4-6 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Theorem 4-7 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem 4-8 If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. Corollary for Theorem 4-8 A line that contains the midpoint of one side of a triangle and is parallel to another side bisects the third side. Theorem 4-9 The Diagonals of a rectangle are congruent Theorem 4-10 The diagonals of a rhombus are perpendicular Theorem 4-11 Each diagonal of a rhombus bisects two angles of the Rhombus Theorem 4-12 The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices. Theorem 4-13 If a angle of a parallelogram is a right angle, then the parallelogram is a rectangle Theorem 4-14 If two consecutive sides of a parallelogram are congruent, then he parallelogram is a rhombus. Theorem 4-15 Base angles of an isosceles trapezoid are congruent. Theorem 4-16 The median of a trapezoid: (1) is parallel to the bases. (2) has the length equal to half the sum of the lengths of the bases. Theorem 4-17 The segment that joins the midpoints of two sides of a triangle: (1) is parallel to the third side; (2) has a length equal to the half of the length of the third side. Theorem 4-18 If one side of a triangle is larger than a second side, then the angle opposite the first angle is longer than the side opposite the second angle Theorem 4-19 If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. Corollaries for Theorem 4-19 Corollary 1 The perpendicular segment from a point to a line is the shortest segment from the point to the line. Corollary 2 The perpendicular segment from a point to a plane is the shortest segment from the point to the plane Theorem 4-20 The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Theorem 4-21 SAS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side f the second triangle. Theorem 4-22 SSS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second then the included angle of the first triangle is larger than the included angle of the second. Definitions : Parallelogram : is a quadrilateral with both pairs of opposite sides parallel. Rectangle : a quadrilateral with four right angles Rhombus : a quadrilateral with four congruent sides. Square : a quadrilateral with four right angles and four congruent sides. Trapezoid : a quadrilateral with exactly one pair of parallel sides Bases : The parallel sides of a trapezoid. Legs : the other sides of a trapezoid that are not parallel. Isosceles : a trapezoid with congruent legs.