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Geometry Mr. Rasiej

Geometry Mr. Rasiej. Feb. 2011 Final Review. Points, Lines, Planes, Angles. Line, segment, ray Complementary, supplementary Collinear, coplanar Acute, right, obtuse Angle bisector, perpendicular bisector Vertical angles, skew lines Midpoint of a segment. Congruent Triangles.

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Geometry Mr. Rasiej

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  1. GeometryMr. Rasiej Feb. 2011 Final Review

  2. Points, Lines, Planes, Angles • Line, segment, ray • Complementary, supplementary • Collinear, coplanar • Acute, right, obtuse • Angle bisector, perpendicular bisector • Vertical angles, skew lines • Midpoint of a segment

  3. Congruent Triangles • Corresponding parts (be able to identify) • SSS Postulate, SAS Postulate, ASA Postulate, AAS Theorem, HL Theorem • CPCTC (remember the cha-cha)

  4. Isosceles and Equilateral Triangles • 2 sides congruent >>> base angles congruent (and vice-versa) • Vertex angle • All 3 angles in an equilateral triangle have measure = 60 Degrees (all 3 sides have same length) • Any exterior angle to a triangle is equal in measure to the two interior angles at the opposite vertices (also called remote interior angles).

  5. Inequalities in One Triangle The measure of an exterior angle is greater than the measure of each of its remote interior angles If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle THE SUM OF THE LENGTHS OF ANY TWO SIDES OF A TRIANGLE IS GREATER THAN THE LENGTH OF THE THIRD SIDE

  6. Parallel Lines • Know the meaning of: • Corresponding angles, alternate exterior angles, alternate interior angles, same side exterior angles, same side interior angles, transversal

  7. Angle Measure in a Triangle • Sum of the measures of the 3 angles is 180 degrees • If the ratio of the three angles is given as a:b:c then you find the measures of the three angles by ax + bx + cx = 180 x(a+b+c)=180, so x=180/(a+b+c) Then the three angles are ax, bx, cx.

  8. Polygons • A (convex) polygon with n sides is also referred to as an n-gon • Understand exterior angle of a polygon. Sum of all exterior angles of a convex n-gon is 360. Sum of all interior angles of a convex n-gon is (n-2) x 180 (so, 180 for a triangle (3-gon), 360 for a square (4-gon), 540 for a pentagon (5-gon),etc.)

  9. Quadrilaterals • Know the properties of • Parallelograms • Rectangle • Rhombus • Square • Trapezoid, including isosceles trapezoid, midsegment of trapezoid • Kite • Know what is true about the diagonals for each quadrilateral.

  10. Similarity • If angles of two polygons are congruent and their corresponding sides are in proportion, they are called similar. • For triangles, • AA similarity postulate • SAS similarity theorem • SSS similarity theorem • Understanding the properties of proportions (p. 367) very important

  11. Coordinate Geometry • Know the formulas for • Slope • Distance • Midpoint • Lines and segments are parallel if their slopes are equal. • Lines and segments are perpendicular if the product of their slopes is -1 (OR, which is the same thing, if the slope of one is the opposite of the reciprocal of the other).

  12. Good Sample Problems to DO • Finish working on the two final review packs. Each one is a double homework, so doing both gets you 16 points. • P. 192 3 – 14 • P. 253 1 – 12, 15, 16 • P. 300 7 – 9, 11 – 14 • P. 361 1 – 18 • P. 375 1 - 16

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