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Transcript
Midterm Review: Topic and Definitions Chapter 1 Main Topics: 1.1: Points, Lines and Planes 1.2: Segments and Rays 1.3: Distance and Midpoint Formulas 1.4: Angles 1.5: Parallel and Perpendicular Lines Define and give an example: Point: Object that does not have an actual size Line: Extend indefinitely and have no thickness or width Collinear Points: Points that lie on the same line Plane: a flat surface that extends indefinitely in all directions Intersection: the set of points that is common for two given figures Coplanar: Objects that lie on the same plane Segment: part of a line that consists of two endpoints and all of the points in between Segment Addition Postulate: If C is between A and B, then AC + CB = AB Congruent Segments: Segments with equal lengths Ray: part of a line, has one fixed endpoint, and extends infinitely along the line from the endpoint. Opposite Rays: rays with a common endpoint, extending in opposite directions and forming a line. Distance Formula: Midpoint Formula: Bisector: the line that divides something into two equal parts Angle: a figure formed by two rays with a common endpoint Vertex: common endpoint of an angle Acute Angle: an angle whose measure is less than 90 degrees Right Angle: an angle whose measure = 90 degrees Obtuse Angle: an angle whose measure is bigger than 90 degrees but less than 180 degrees Straight Angle: an angle that is 180 degrees Angle Addition Postulate: The sum of two parts of an angle will equal the whole angle Congruent Angles: two angles with the same measurement Angle Bisector: a ray in the interior of the angle that divides the angle into two congruent angles How to find slope of a graph: How to find slope of ordered pairs: Parallel Equations: two equations that have the same slope and different y-intercepts; their graphs will never intersect Perpendicular Equations: The equations have slopes that are opposite reciprocals; their graphs cross to form a right angle Opposite Reciprocals: two numbers that have opposite signs and are flipped fractions of each other. Chapter 3 Main Topics: 3.1: Angle Relationships 3.2: Identify Pairs of Lines and Angles 3.3a: Angles and Parallel Lines 3.3b: Proving Lines Parallel Define and give an example: Complementary angles: When two angles add up to 90 degrees Supplementary angles: When two angles add up to 180 degrees Adjacent angles: two angles that share a common vertex and side but have no common interior points Linear Pair: two adjacent angles that are supplementary Vertical angles: a pair of angles whose sides form opposite rays Corresponding angles: pairs angles that have corresponding locations when two lines are cut by a transversal Alternate interior angles: pairs of angles in the interior on opposite sides of the transversal Alternate exterior angles: pairs of angles in the exterior of two lines cut by a transversal on opposite sides Consecutive interior angles: pairs of interior angles on the same side of the transversal Transversal: a line that intersects two or more lines in a plane at different points Chapter 4 Main Topics: 4.1: Intro to Triangles 4.2: Congruent Triangles 4.3: Isosceles Triangles 4.4: Triangle Inequalities Define and give an example: Acute triangle: triangle with three acute angles Right triangle: triangle with one right angle. The other two angles are acute and complementary Obtuse triangle: triangle with one obtuse angle Equiangular triangle: triangle with three congruent angles Isosceles triangle: a triangle with at least two congruent sides Scalene triangle: a triangle with no congruent sides Equilateral triangle: a triangle with all congruent sides Isosceles triangle theorem: If two sides of a triangle are congruent, then the angles opposite of them are also congruent Legs in an isosceles triangle: The two congruent sides Base angles in an isosceles triangle: The two congruent angles Base of an isosceles triangle: the side that is formed by the two base angles Chapter 5 Main Ideas 5.1: Proving Triangles Congruent 5.2: Using Proofs with Triangles Define: CPCTC: corresponding parts of congruent triangles are congruent Name the 5 congruent triangle postulates: SSS, SAS, AAS, ASA, HL Reflexive property: any quality equal to itself Symmetric property: if one quantity is equal to a 2nd quantity, then the 2nd quantity is equal to the first Chapter 6 Main Ideas: 6.1: Similar Polygons 6.2: Proving Triangles Similar Through AA 6.3: Mid-segment of a Triangle 6.4: Partitioning a Line Segment Define: Similar figures: two polygons are similar iff their corresponding angles are congruent and lengths of corresponding sides are proportional Proportional: lengths of sides are proportional iff the ratios of the lengths of corresponding sides are equal Scale factor: The ratio of corresponding sides of similar polygons AA Similarity: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar Mid-segment of a triangle: a segment joining the midpoints of two sides of a triangle Property 1 of a mid-segment: a mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle Property 2 of a mid-segment: the mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle