T103 Final Review Sheet. Central Angles. Inductive Proof. Transversal. Rectangle

Transcription

1 T103 Final Review Sheet Know the following definitions and their notations: Point Hexa- Space Hepta- Line Octa- Plane Nona- Collinear Deca- Coplanar Dodeca- Intersect Icosa- Point of Intersection Interior Angle Segment Exterior Angle Length Measure Central Angles Congruent Segments Equilateral Triangle Midpoint of a Segment Equiangular Triangle Bisector of a Segment Isosceles Triangle Ray Scalene Triangle Angle Right Triangle Degree measure Acute Triangle Straight Angle Obtuse Triangle Zero Angle Median Angle Bisector Altitude Right Angle Vertices Acute Angle Edges Obtuse Angle Inductive Proof Complementary Angles Deductive Proof Supplementary Angles Counterexample Adjacent Angles Transversal Consecutive Angles Parallel Lines Linear Pair of Angles Alternate Angles Vertical Angles Same-Side Angles Perpendicular Lines Interior Angles Perpendicular Bisector Exterior Angles Polygons Corresponding Angles Triangle Arc Quadrilateral Parallelogram Penta- Rectangle Rhombus Square Trapezoid Kite Construction Compass Straight Edge Reflectional Symmetry Rotational Symmetry Point Symmetry Polyhedron Prism Pyramid English System Metric System Length Area Volume Mass (Weight) Time Temperature Fahrenheit Celsius Perimeter Circle Radius Diameter Circumference Ratio Surface Area Volume

2 **Note: You should be able to prove (or give a good explanation for) any highlighted theorems or properties (without using the theorem or property itself) Any topic in pink WILL be on at least one problem on the final 10.1 Use vocabulary correctly and with proper labels and be able to draw figures. Understand the Fibonacci Sequence and how it is constructed as well as how it relates to the golden ratio Prove or find counterexamples for a given statement 10.2 Understand Network Traversability o Draw out a network when not drawn (Ex. #48 p549) o When is a network traversable type 1? o When is a network traversable type 2? o Change an existing network to make it traversable 10.3 Angle Congruencies in Parallel Lines Theorem Sum of the Measures of Interior Angles Theorem for Triangle o Sum of the Measures of Interior Angles Theorem for Polygons Measure of Interior Angles for a regular polygon Sum of the Measures of Central Angles Theorem for Polygons o Measure of Central Angles for a regular polygon Sum of the Measures of Exterior Angles Theorem for Polygons o Measure of Exterior Angles for a regular polygon Use the formulas relating arc measures and angle measures for P o Inside the circle o On the circle o Outside the circle Solve algebraic/word problems from this chapter similar to #3-5,39,40,41, Congruent Triangles o Vertices must be in the correct order in the congruence statement o Each of the three congruent parts should be labeled. o SSS, SAS,ASA Postulates o AAS,HA,HL Theorems Pythagorean Theorem o Use in 2- and 3- dimensional situations o Complete right triangles when not drawn in (Ex. #66) o Find missing sides of a triangle o Find missing sides of a triangle

3 10.5 *Should be able to prove any one property using the other properties A quadrilateral is a parallelogram if and only if o Opposite sides are parallel o Opposite sides are congruent o One pair of opposite sides is both congruent and parallel o Opposite angles are congruent o Consecutive angles are supplementary o Its diagonals bisect each other A quadrilateral is a rectangle if and only if o It has 4 right angles o It is a parallelogram with one right angle o It is a parallelogram with congruent diagonals A quadrilateral is a rhombus if and only if o It has 4 congruent sides o Its diagonals bisect the angles o It diagonals are perpendicular bisectors of each other A quadrilateral is a square if and only if o It has 4 congruent sides and 4 right angles o It is a rectangle with 4 congruent sides o It is a rhombus with a right angle o It diagonals are congruent and perpendicular bisectors of each other A quadrilateral is a kite if and only if o It has 2 mutually exclusive pairs of adjacent sides congruent A quadrilateral is a trapezoid if and only if o It has exactly one pair of parallel sides Constructions: Be able to construct the following and prove they construct what they claim to o a congruent segment o an angle o a triangle o a perpendicular bisector to a segment o an angle bisector o a parallel line o an equilateral triangle o a right triangle (including and ) o a rectangle (including a square) o a parallelogram (including a rhombus)

4 11.1 Determine symmetries o Reflectional (2D) needs the line of reflection (drawn or described) o Rotational (2D) needs a center (point) and an angle o Point symmetry needs a point (same as 180 degree rotational) 11.4 Know names of polyhedra (do not need to memorize shapes of the faces) Be able to truncate any polyhedron Use Euler s Formula Determine symmetries o Reflectional (3D) needs the plane of reflection (drawn or described) o Rotational (2D) needs a center (line) and an angle 12.1 Know and use all conversions highlighted on the measurement sheet You should also know that 1cm 3 = 1 ml for water. Convert temperatures from Fahrenheit to Celsius and back Know whether length, mass, temperature, time, and volume of an object are reasonable (see #69-73) (ex. a temperature of -40 degree Celsius is not reasonable to serve a cooked steak and a swimming pool cannot have 3 cups of water in it. These will be extreme when wrong) 12.2 On highlighted formulas, make sure you can explain how we can derive this formula (you can use earlier formulae) Know how to use the following formula in both simple pictures and word problems (#46-60) Perimeters o Square o Rectangle o Parallelogram o Triangle o Regular Polygon o Circle (Circumference) Areas o Rectangle o Square o Triangle (including equilateral) o Parallelogram o Trapezoid o Regular polygon o Circle

5 12.3 Surface Areas o Prisms (including rectangular and cubes) o Cylinder o Pyramid (should also be able to do rectangular bases) o Cone o Sphere Volumes o Prisms (including rectangular and cubes) o Cylinder o Pyramid o Cone o Sphere There will be at least one problem, and most likely two or more from this section since it has not been on any quizzes or exams (and also because it puts together pieces from several other sections) (#1-48)