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November 30, 2012 Welcome to Class! Write down the assignment in your agenda Get a blue math book PROBLEM OF THE WEEK! November 30, 2012 6th Grade Module 3 Unit 1 Day 1 Notes GEOMETRY Vocabulary: Point-‐ an exact loca*on, represented by a ______________ Line-‐ a straight path through __________ extending forever in opposite direc*ons Ray-‐ part of a line, has one _____________ and extends in the Line segment-‐ part of a line, with ____________endpoints other direc*ons Plane-‐ ﬂat surface that has _________ thickness, extends forever Congruent-‐ ﬁgures with ___________shape and size (EQUAL) Angle-‐ two _______________with a common endpoint Vertex-‐ the common ________________________ Right angle-‐ _____________angle Acute angle-‐ angle measuring greater than ____________ and less than _____________ Obtuse angle-‐ angle measuring greater than ________________ Straight angle-‐ _________________angle and less than ______________________ Complementary angles-‐ the ________of two angles is Supplementary angles-‐ the __________of two angles is _______________ ____________________ Example 1: List: three points K M three lines N a plane J L three rays three line segments Example 2: Find the measure of each angle and describe the R angle type. a) PQR S b) RQS 60o P 90o 30o 30o c) UQR Q T d) PQT U Use the figure to complete the statements. a) ≮RQS and ≮SQT are ________________________________angles b) ≮PQS and ≮SQT are ________________________________angles November 30, 2012 Welcome to Class! Write down the assignment in your agenda Get a blue math book Put your homework on the top left corner of your desk PROBLEM OF THE WEEK! November 30, 2012 Line and Angle Relationships Notes Geometry Vocabulary: Perpendicular lines-‐ lines that intersect at _______________angles Parallel lines-‐ lines in the same plane that do not __________________ Skew lines-‐ lines that do not intersect and are not ________________ Adjacent angles-‐ two angles that share a (they are in diﬀerent planes!) ______________and _________________, but no common interior points VerFcal angles-‐ ____________________angles formed when two lines Transversal-‐ a line that ___________________two or intersect. more lines that lie on the same plane Corresponding angles-‐ angles in corresponding ____________________ Interior angles-‐ angles __________________ the two (In the same posi*on in rela*on to the transversal) parallel lines (with transversal) Alternate interior angles-‐ interior angles on ____________________ sides Exterior angles-‐ angles ___________________the of the transversal parallel lines (with transversal) Alternate exterior angles-‐ exterior angles on _____________________ Sides of the transversal Example 1: Identifying Adjacent Angles a) Name all pairs of adjacent, supplementary angles. 1 4 2 3 b) Name the vertical angles. Example 2: Using Vertical Angles a) Given that m≮1 = 75o, find m≮3. 1 2 4 3 b) Find the m≮2. c) Find the m≮4. d) Name 2 adjacent, supplementary angles. November 30, 2012 Welcome to Class! Write down the assignment in your agenda Put your homework on the top left corner of your desk PROBLEM OF THE WEEK! November 30, 2012 Review Line and Angle Relationships Notes Example 1: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines in the figure appear parallel, perpendicular, or skew. a) AB and AC b) CG and BD c) AC and BD Example 2: Using Angle Relationships to Find Angle Measures Line n ll p. Find the measure of each angle. ≮1 ≮4 ≮2 ≮5 ≮3 ≮6 November 30, 2012 Welcome to Class! Write down the assignment in your agenda Put your homework on the top left corner of your desk Come see me to pass back papers PROBLEM OF THE WEEK! November 30, 2012 Classifying Polygons Notes Geometry Vocabulary: Polygon- a simple, closed plane figure formed by Regular polygon- polygon with all sides and all ___________ or more line segments angles ____________ Examples: Non-Examples: Example 1: Determine whether each figure is a polygon. It if is not, explain why not. Example 2: Name each polygon. Example 3: Name each polygon and tell whether it is a regular polygon. If it is not, explain why not. November 30, 2012 Welcome to Class! Write down the assignment in your agenda Put your homework on the top left corner of your desk Come see me to pass back papers Get a blue math book PROBLEM OF THE WEEK! November 30, 2012 Classifying Triangles Notes Example 1: Classify each triangle by its sides and then by its angle measures. Example 2: Identify the different types of triangles in the figure, and determine how many of each there are. November 30, 2012 Welcome to Class! Write down the assignment in your agenda Come see me to pass back papers Get a blue math book PROBLEM OF THE WEEK! November 30, 2012 Classifying Quadrilaterals Notes Geometry Vocabulary: Parallelogram- quadrilateral with opposite sides _____________and _______________. (Opposite angles are ≅) Rectangle- parallelogram with ______________right angles and ______________________ sides are congruent. Rhombus- parallelogram with _____________congruent sides. Square- parallelogram with ______________congruent sides and four _________________angles. Trapezoid- exactly one pair of opposite sides is ______________ Example 1: Give all of the names that apply to each quadrilateral. Then give the name that best describes it. Example 2: Draw each figure. If it is not possible to draw, explain why. a) A rectangle that is not a square. b) A rectangle that is not a parallelogram. November 30, 2012 Welcome to Class! Write down the assignment in your agenda Put your homework on the top left corner of your desk Come see me to pass back papers PROBLEM OF THE WEEK! November 30, 2012 Interior Angle Sums of Triangles and Quadrilaterals Notes The sum of the angles in a triangle equal 180˚ Find the unknown angle measure in the triangle. Example 1: Example 2: Example 3: A right triangle with one angle measure of 36o The sum of the angles in a quadrilateral equal 360˚ Find the unknown angle measure in the quadrilateral. Example 4: Example 5: Example 6: A quadrilateral with angle measures of 144o, 84o, and 48o November 30, 2012 Welcome to Class! Write down the assignment in your agenda Put your homework on the top left corner of your desk Come see me to pass back papers PROBLEM OF THE WEEK! November 30, 2012 Interior Angles of Polygons Notes Triangle- interior angles equal _____________________ Quadrilateral- interior angles equal ________________________ All polygons- divide it into triangles, multiply ______________________ by the number of triangles Example 1: Divide the polygon into triangles to find the sum of its angle measures. Example 2: Find the sum of the interior angles of each polygon. Example 3: Number of Number of Figure Sides Triangles Quadrilateral 4 Pentagon 5 Hexagon 6 **The number of triangles is always 2 less than the number of sides of the figure. Example 4: Find the sum of the interior angles. November 30, 2012 November 30, 2012 Welcome to Class! Write the assignment in your agenda Put your homework on the top left corner of your desk Come see me to pass back papers Get a blue math book PROBLEM OF THE WEEK! November 30, 2012 Similar and Congruent Figures Notes Similar figures- figures with the same ______________________, but not the same size Congruent figures- similar figures that have the same ____________ AND the same ___________ Corresponding angles- angles that are in the same _______________________ in the shape Corresponding sides- sides that are in the same _______________________ in the shape Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. Example 1: Are these figures similar? a) b) Example 2: Find the unknown measure in the similar figures. a) b) Example 3: Determine whether the figures are congruent. Example 4: Determine the unknown measure in each set of congruent polygons. November 30, 2012 Welcome to Class! Write down the assignment in your agenda Put your homework on the top left corner of your desk Come see me to pass back papers ISTEP Packet PROBLEM OF THE WEEK! November 30, 2012 Transformations and Symmetry Notes Transformations- changing the ______________________of a geometric figure Types of Transformations Translation- __________________ Reflection- ___________________ Rotation- __________________ Example 1: Name the transformation in each figure. Example 2: Decide whether each of the figures has line symmetry. If it does, draw all the lines of symmetry. Line Symmetry- drawing a line down the _____________________of a figure, producing the exact same image on both sides of the line Rotational Symmetry- figure is rotated less than 360o and it is the original shape Example 3: Tell how many times each figure will show rotational symmetry within one full rotation. November 30, 2012 Welcome to Class! Write down the assignment in your agenda Come see me to pass back papers Review for your homework quiz PROBLEM OF THE WEEK! November 30, 2012 Welcome to Class! Write down the assignment in your agenda Come see me to pass back papers Ask any last minute questions PROBLEM OF THE WEEK! GOOD LUCK November 30, 2012

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posted: | 11/30/2012 |

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