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Transcript
Unit 3 Prior Vocabulary Gallery Adjacent Angles Angles in the same plane that have a common vertex and a common side, but no common interior points. In the figure above, angle FKI and angle FKH are adjacent angles. Transversal A line that crosses two or more lines. Alternate Interior Angles Pairs of angles formed when a third line (transversal) crosses two other lines and are on opposite sides of the transversal and are in between the other two lines. Angles 1,2,3, and 4 are interior angles. Angles 1 and 4 are alternate interior angles. Angles 2 and 3 are also alternate interior angles. Line t (in red) is called a transversal, a line crossing two or more lines. Same-Side Interior Angles Pairs of angles formed when a transversal (a third line) crosses two other lines. These angles are on the same side of the transversal and are outside the other two lines. Angles 1 and 3 are same-side interior angles and angles 2 and 4 are same-side interior angles. Alternate Exterior Angles: Pairs of angles formed when a transversal Crosses two other lines and are on opposite sides of the transversal and are Outside the other two lines. Angles 1, 2, 3, and 4 are all exterior angles. Angles 1 and 4 are alternate exterior angles. Angles 2 and 3 are also alternate exterior angles. Line t (in red) is called a transversal, a line Crossing two or more lines. Complementary Angles Two angles whose sum is 90º. In the example to the right, notice that at all times, angle BAT + angle CAT = 90º.The diagram to the left is the typical representation of complementary angle, but the angles do not have to be adjacent (as shown here) to be complementary. Congruent Having the same size, shape and measure. Notice that each figure below is congruent to one other figure in the given set of figures. The congruent pairs are congruent because they have the same size and shape, regardless of their orientation (the way they are "sitting"). Corresponding Angles Angles that have the same relative positions in geometric figures. For example, in the figure below there are two triangles: a larger triangle, ABC, and a smaller triangle, ADE. Angles ADE and ABC are corresponding because they both lie in the same relative position in the two triangles. Angles ABC and AED are not corresponding since they do not lie in the same Relative position in the two triangles. Equiangular The property of a polygon whose angles are all congruent. For example, an equilateral triangle is equiangular since its interior angles are equal (to 60 degrees). In general, all regular polygons such as equilateral triangle, square, pentagon, and hexagon are equiangular. Equilateral The property of a polygon whose sides are all congruent. Regular Polygon A polygon that is both equilateral and equiangular. Intersecting Lines Two lines in a plane that cross each other. Two distinct lines intersect if they do not have the same slope. In other words, if the slopes are same (i.e., lines are parallel), they do not intersect each other. Linear Pair Adjacent, supplementary angles. A linear pair forms a straight line. Remember that, by definition, segment AC is part of a straight line. Angles ABG and CBG are adjacent angles (since they share side BG). The other side of each angle, sides AB and BC, form the line segment AC. Therefore; we can call angles ABG and CBG a linear pair. Parallel Lines Two lines that lie in the same plane and they do not intersect. Two lines that lie in the Same plane and they do not intersect. In the following example, the two red lines (k and l) are parallel lines. Parallel lines Are written using the symbol | |. In this case k | | l. Perpendicular Lines Two lines that intersect at a right angle. Skew Lines Two lines that do not lie in the same plane and never intersect and are not parallel. Supplementary Angles Two angles whose sum is 180. Notice that since angle ABC is a straight angle, meaning that its measure is 180 degrees, then angle ABG + angle CBG = 180 degrees. Therefore, we can say that angles ABG and CBG are supplementary. Vertical Angles Two nonadjacent angles formed by intersecting lines or segments. Also called opposite angles. In the above example, angles EKG and HKF are opposite angles because their sides are formed by two intersecting segments (EF & GH). Notice that the angles have only one point in common, the vertex (K).