Geometry Chapter 3 Parallel Lines and Perpendicular Lines Pages 124 - 195

Download Geometry Chapter 3 Parallel Lines and Perpendicular Lines Pages 124 - 195

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<ul><li><p>Geometry Chapter 3 Parallel Lines and Perpendicular LinesPages 124 - 195</p></li><li><p>3-1 PAIRS &amp; LINES OF ANGELSWhat you will learn: Identify lines and planesIdentify parallel and perpendicular linesIdentify pairs of angles formed by transversals</p></li><li><p>3-1 PROPERTIES OF PARALLEL LINESEssential Question: What does it mean when two lines are parallel, intersecting, coincident, or skew?</p></li><li><p>PREVIOUS VOCABULARYPerpendicular lines</p></li><li><p>CORE VOCABULARY</p></li><li><p>PARALLEL LINESTwo lines that do not intersectGo in same directionCoplanar</p></li><li><p>SKEW LINESTwo lines that do not intersectAre not coplanar</p></li><li><p>PARALLEL PLANESTwo planes that do not intersect</p></li><li><p>TRANSVERSALA line that intersects two or more coplanar parallel lines</p></li><li><p>CORRESPONDING ANGLESCongruentSame positionDifferent location</p></li><li><p>ALTERNATE INTERIOR ANGLESCongruentInsideOpposites sides</p></li><li><p>ALTERNATE EXTERIOR ANGLESCongruentOutsideOpposites sides</p></li><li><p>SAME-SIDE (consecutive) INTERIOR ANGLESSupplementaryInsideSame side</p></li><li><p>PARALLEL LINESTwo coplanar lines that do not intersect</p></li><li><p>STRAIGHT ANGLEExactly 180 degrees</p></li><li><p>VERTICAL ANGLES2 angles directly across from each othercongruent</p></li><li><p>SUPPLEMENTARY ANGLESTwo angles whose measures add up to 180 degrees</p></li><li><p>3 2 PARALLEL LINES &amp; TRANSVERSALSWhat you will learn:Use properties of parallel linesProve theorems about parallel linesSolve real-life problems </p></li><li><p>3-2 PARALLEL LINES &amp; TRANSVERSALSEssential Question: When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? </p></li><li><p>CORE VOCABULARY</p></li><li><p>TRANSVERSALA line that intersects two or more coplanar parallel lines</p></li><li><p>CORRESPONDING ANGLESCongruentSame positionDifferent location</p></li><li><p>ALTERNATE INTERIOR ANGLESCongruentInsideOpposites sides</p></li><li><p>ALTERNATE EXTERIOR ANGLESCongruentOutsideOpposites sides</p></li><li><p>SAME-SIDE (consecutive) INTERIOR ANGLESSupplementaryInsideSame side</p></li><li><p>3 3 Proofs and Parallel LinesWhat you will learn:Use the Corresponding Angles ConverseConstruct Parallel LinesProve theorems about parallel linesUse Transitive Property of Parallel Lines</p></li><li><p>3 3 Proofs and Parallel LinesEssential Question: Name the two types of pairs of angles that are supplementary</p></li><li><p>WAYS TO PROVE TWO LINES PARALLELShow that a pair of corresponding angles are congruentShow that a pair of alternate interior or exterior angles are congruentShow that a pair of same-side interior angles are supplementary</p></li><li><p>WAYS TO PROVE TWO LINES PARALLELShow that both lines are perpendicular to a third lineShow that both lines are parallel to a third line</p></li><li><p>Core Concept:Five Types of Angle PairsCorresponding Alternate Interior Alternate Exterior Same-Side Interior 180Vertical Linear Pair 180</p></li><li><p>PERPENDICULAR LINESTwo lines that intersect to form right anglesIf a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line</p></li><li><p>3 - 4 PROOFS WITH PERPENDICULAR LINESWhat you will learn: Find the distance from a point to a lineConstruct Perpendicular linesProve theorems about perpendicular linesSolve real life problems involving perpendicular lines</p></li><li><p>3 4 Proofs and Parallel LinesEssential Question: What conjectures can you make about perpendicular lines?</p></li><li><p>VOCABULARYDistance from a point to a linePerpendicular bisector</p></li><li><p>Distance from a point to a lineThe length of the perpendicular segment from the point to the line</p></li><li><p>Perpendicular BisectorA perpendicular bisector of a line segment is a line segment that is perpendicular to the segment at its midpoint</p></li><li><p>PARALLEL LINESTwo lines that do not intersectGo in same directionIf two lines are parallel to the same line, they are parallel to each otherIf two lines are perpendicular to the same line, then they are parallel to each other</p></li><li><p>TRIANGLEThree sidesInterior angle sum is 180 Symbol: Sides are called segmentsEach point is a vertex</p></li><li><p>EQUIANGULARAll angles are 60</p></li><li><p>ACUTE TRIANGLE</p><p>Three angles less than 90 degrees</p></li><li><p>RIGHT TRIANGLEOne right angle</p></li><li><p>OBTUSE TRIANGLE</p><p>One obtuse angle</p></li><li><p>EQUILATERAL TRIANGLEAll sides congruent</p></li><li><p>ISOSCELES TRIANGLEAt least two congruent sides</p></li><li><p>SCALENE TRIANGLE</p><p>No congruent sides</p></li><li><p>EXTERIOR ANGLEOutside the triangleEquals the remote interior angles Supplementary to its adjacent angle</p></li><li><p>REMOTE INTERIOR ANGLESon the opposite side of the exterior anglesequal the measure of the exterior angle</p></li><li><p>3 - 5 POLYGON ANGLE-SUM THEOREMSTANDARD: classify polygons find measures of interior and exterior angles of polygons</p></li><li><p>VOCABULARYPolygonConcave PolygonConvex PolygonDiagonalPolygon Angle SumPolygon Exterior Angle SumEquilateral PolygonEquiangular PolygonRegular Polygon</p></li><li><p>POLYGONClosed plane figureAt least 3 sides and anglesClassified by the number of sides</p></li><li><p>CONVEX POLYGONDoesnt cave in</p></li><li><p>CONCAVE POLYGONcaves in</p></li><li><p>DiagonalConnects vertices</p></li><li><p>POLYGON ANGLE SUM (n-2)180</p></li><li><p>POLYGON EXTERIOR ANGLE SUM The exterior angles of a polygon = 360</p></li><li><p>EQUILATERAL POLYGONAll sides are congruent</p></li><li><p>EQUIANGULAR POLYGON*All angles are congruent</p></li><li><p>REGULAR POLYGON EquiangularEquilateral</p></li><li><p>3 - 6 LINES IN THE COORDINATE PLANESTANDARD: graph lines given their equations to write equations of lines</p></li><li><p>VOCABULARYSlopey-interceptx-interceptGraphing Using InterceptsStandard FormSlope Intercept FormPoint Slope Form</p></li><li><p>SLOPE</p></li><li><p>y-interceptWhere the graph intersects the y-axis</p></li><li><p>x-interceptWhere the graph intersects the x-axis</p></li><li><p>Graphing Using interceptsSubstitute 0 for x and y to find the intercepts</p></li><li><p>STANDARD FORMAx + By = C</p></li><li><p>SLOPE INTERCEPT FORMy = mx + bb = y-interceptm = slope</p></li><li><p>POINT SLOPE FORMy - y1 = m(x - x1)</p></li><li><p>3 - 7 SLOPES OF PARALLEL AND PERPENDICULAR LINESSTANDARD: relate slope and parallel lines relate slope and perpendicular lines</p></li><li><p>PARALLEL LINESHave equal slopesTwo lines that do not intersectGo in same direction</p></li><li><p>PERPENDICULAR LINESThe product of slopes is -1Two lines that intersect to form right angles</p></li><li><p>SLOPE INTERCEPT FORMy = mx + bb = y-interceptm = slope</p></li><li><p>INTERSECTTo cutDivide by passing through</p></li><li><p>CONGRUENTequalThe same</p></li></ul>

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