Properties of Parallel Lines Name(s): In this investigation, you’ll discover relationships among the angles formed when parallel lines are intersected by a third line, called a Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. The property derived from this is the ratio of intercepts which is proved using similar triangles. Parallel lines preserve the ratio of intercepts on transversals. GEO 3-2 Properties of Parallel Lines.pdf. Shape Name Property Also looks like corresponding angles Corresponding angles are equal α = θ co-interior angles Co-interior angles are supplementary α + θ = 180° alternate angles Alternate angles are equal α = θ. a b 4 115° (x + 5)° SOLUTION By the Vertical Angles Congruence Theorem (Theorem 2.6), m∠4 = …Īngles and parallel lines When two parallel lines are cut by a transversal (or third line), many of the angles formed have special properties. Section 3.2 Parallel Lines and Transversals 133 Using Properties of Parallel Lines Find the value of x. Students will reason and evaluate mathematical arguments. Apply properties of angle pairs formed by parallel lines cut by a transversal.
Investigate characteristics of parallel lines both algebraically and geometrically. Section 2.2 Angles Formed by Parallel Lines menihek.caĪnd apply the properties of parallel and perpendicular lines and understand the meaning of congruence. From the diagram below, angle 4 & 6 and 3 & 5 are sameside interior angles. Use the cut-out to find congruent angles.
Properties of parallel lines 157 using properties of parallel lines using parallel lines in real life will be parallel to the first 32 geometry chapter 3 parallel and perpendicular e quations of lines day 2 3 4 practice worksheet and 3 4 application discovering properties of parallel geometry parallel lines worksheet answers and geometry properties and then we can use these properties parallel Record your responses to the following: a. Investigate the web site and the game rules. Each group chooses one of the web sites given in the Pre-Activity Preparation section. Points, Lines, Angles, and Parallel Lines teAm Activity 1. Theorem: If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary. Theorem: If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent. Properties of Parallel Lines: Postulate: If two parallel lines are intersected by a transversal, then the corresponding angles are congruent. Practice 3-1 Properties of Parallel Lines Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles. Of 8 3.5 What you should learn GOAL 1 Use properties of parallel lines in real-life situations, such as building a CD rack in Example 3.
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