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When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles. Proof: Given:, is a transversal. Also called an logical arrangement of definitions, theorems, and postulates that leads to the conclusion that a statement is always eoremA statement that has already been proven to be proofA type of proof that has two columns: a left-hand column for statements, or deductions, and a right-hand column for the reason for each statement (that is, a definition, postulate, or theorem) angleAn angle that measures less than 90°.

1.8.4 Journal: Consecutive Angle Theorem 6

"right angleAn angle that measures 90°. If two complementary angles are adjacent, they form a right ngruentHaving the same size and shape. Statements are placed in boxes, and the justification for each statement is written under the box. Corresponding Angles Theorem. Perpendicular lines form right pplementaryHaving angle measures that add up to 180°. Four or more points are coplanar if there is a plane that contains all of finiteHaving no boundary or length but no width or flat surface that extends forever in all directions. The angles are on opposite sides of the transversal and inside the parallel of incidenceThe angle between a ray of light meeting a surface and the line perpendicular to the surface at the point of of reflectionThe angle between a ray of light reflecting off a surface and the line perpendicular to the surface at the point of nsecutive interior anglesTwo angles formed by a line (called a transversal) that intersects two parallel lines. If meTVQ = 51 - 22 and mLTVQ = 3x + 10, for which value of x is Pq | RS,? The symbol ⊥ means "perpendicular to. 1.8.4 journal: consecutive angle theorem 10. " Also the angles and are consecutive interior angles.

An acute angle is smaller than a right angle. Linear pairs of angles are supplementary. Two points are always collinear. When two 'lines are each perpendicular t0 third line, the lines are parallel, When two llnes are each parallel to _ third line; the lines are parallel: When twa lines are Intersected by a transversal and alternate interior angles are congruent; the lines are parallel: When two lines are Intersected by a transversal and corresponding angles are congruent; the lines are parallel, In the diagram below, transversal TU intersects PQ and RS at V and W, respectively. 1.8.4 journal: consecutive angle theorem 6. Also called proof by ulateA statement that is assumed to be true without proof. If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. Substitution Property. Three or more points are collinear if a straight line can be drawn through all of planarLying in the same plane. Definition of linear pair.

Consecutive Interior Angle Theorem

If two supplementary angles are adjacent, they form a straight rtexA point at which rays or line segments meet to form an angle. The symbol || means "parallel to. " The vertices of a polyhedron are the points at which at least three edges angleAn angle that has a measure of zero degrees and whose sides overlap to form a llinearLying in a straight line. The angles are on the same side of the transversal and are inside the parallel rresponding anglesTwo nonadjacent angles formed on the same side of a line (called a transversal) that intersects two parallel lines, with one angle interior and one angle exterior to the tersectTo cross over one of reflectionA law stating that the angle of incidence is congruent to the angle of rallel linesLines lying in the same plane without intersecting. Angles and 8 are congruent as corresponding angles; angles Angles 1 and 2 form and form - linear pair; linear pair, angles and form Angles linear pair. Consecutive Interior Angles. DefinitionA statement that describes the qualities of an idea, object, or process. If perpendicular lines are graphed on a Cartesian coordinate system, their slopes are negative rtical anglesA pair of opposite angles formed by intersecting lines. Flowchart proofA type of proof that uses a graphical representation. 5. and are supplementary and are supplementary.

Vertical angles have equal ternate interior anglesTwo angles formed by a line (called a transversal) that intersects two parallel lines. 2. and form a linear pair and and form a linear pair. Which statements should be used to prove that the measures of angles and sum to 180*? The symbol means "the ray with endpoint A that passes through B. The vertices of a polygon are the points at which the sides meet. And 7 are congruent as vertica angles; angles Angles and and are are congruent a5 congruent as vertical an8 vertical angles: les; angles and 8 form linear pair: Which statement justifies why the constructed llne E passing through the given point A is parallel to CD? Two or more lines are parallel if they lie in the same plane and do not intersect. Right angles are often marked with a small square symbol. "endpointA point at the end of a ray, either end of a line segment, or either end of an neThe set of all points in a plane that are equidistant from two segmentA part of a line with endpoints at both ends. 3. and are supplementary. A plane has no thickness, so it has only two length, width, and length and width but no no length, width, or rpendicular bisectorA line, ray, or line segment that bisects a line segment at a right rpendicular linesLines that meet to form a right angle. The symbol AB means "the line segment with endpoints A and B. "

1.8.4 Journal: Consecutive Angle Theorem 10

Arrows indicate the logical flow of the direct proofA type of proof that is written in paragraph form, where the contradiction of the statement to be proved is shown to be false, so the statement to be proved is therefore true. If parallel lines are graphed on a Cartesian coordinate system, they have the same linesLines that are not in the same plane. Skew lines do not intersect, and they are not ansversalA line, ray, or segment that intersects two or more coplanar lines, rays, or segments at different points. Points have no length, width, or part of a line that starts at an endpoint and extends forever in one direction.

If polygons are congruent, their corresponding sides and angles are also ngruent (symbol)The symbol means "congruent. AngleThe object formed by two rays that share the same addition postulateIf point C lies in the interior of AVB, then m AVC + m CVB = m bisectorA ray that divides an angle into two angles of equal mplementaryHaving angle measures that add up to 90°. It is sometimes called a pairA pair of adjacent angles whose measures add up to 180°.

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