MATH 1312 Syllabus

Course Objectives

 Chapter.Section Objective and Example Material Covered 1.1 Define and use logical reasoning and valid statements to develop formal proofs. Week 1 Example:  Given the statement "If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus", state the hypothesis and the conclusion. 1.2 Define and construct lines, rays, and angles given a set of conditions. Week 1 Example:  Which symbols correctly name the angle shown?                                                              a)

 Chapter.Section Objective and Examples Material Covered 1.6       2.1         2.3 Define and construct perpendicular lines, and use the parallel postulate. Week 3       Week 4       Week 4 Example 1:  Given: Point N on line s                     Construct:  Line s, point N, and line m through N so that m is perpendicular to line s.   Example 2: Suppose that r is parallel to s in the figure shown and m<2=87o.    Find           a) m<3    b)    m<6   Example 3: Determine the value of x so that line r will be parallel to line s in the figure shown given that m<4 = 5x and m<5 = 4(x + 5). 2.2 Define conditional, converse, inverse and contrapositive and write an indirect geometric proof. Week 4 Example 1: Write the converse, the inverse, and the contrapositive of the statement, "Two angles are complementary if the sum of their measures is 90o."   Example 2: Which one of the following statements would you prove by the indirect method? a)   In triangle ABC, if m

 Chapter.Section Objective and Examples Material Covered 2.6 Define symmetry with respect to a line and a point and use transformations on geometric figures. Week 5 Example 1: Which words have a vertical line of symmetry?        DAD    MOM      NUN    EYE   Example 2: Given a random geometrical figure, does the following pair of transformations lead to an image that repeats the original figure?  Figure is rotated clockwise about a point 180o twice. 3.1                       3.2 Prove and define congruent triangles and congruent parts of triangles. Week 6                       Week 6 Example 1: In the figure below, the triangles to be proved congruent have been redrawn separately.  Congruent parts are marked.  (a)    Name an additional pair of parts that are congruent by Identity. (b)   Considering the congruent parts, state the reason why the triangles must be congruent.           Example 2: After proving the triangles congruent, use CPCTC to prove the following. Given:

 Chapter.Section Objective and Examples Material Covered 4.1           4.2 Define and use the properties of parallelograms and kites. Week 8           Week 8 Example 1: Given that m

 Chapter.Section Objective and Examples Material Covered 5.2     5.3 Define and prove similar triangles and polygons. Week 10     Week 10 Example 1: Quadrilateral MNPQ ~ quadrilateral RSTU, if MN = 5, NP = n, RS = 10, and ST = n + 3, find n.   Example 2: Classify the following statement as true or false.  If the vertex angles of two isosceles triangles are congruent, then the triangles are similar. 5.4     5.5 Use the Pythagorean theorem and define special right triangles. Week 11     Week 11 Example 1: Determine whether the triple (3, 4, 5) is a Pythagorean triple.   Example 2: Given: Triangle NQM with angles shown in the drawing with line MP perpendicular to NQ.  Find: NM, MP, MQ, PQ, and NQ. 6.1 Define and construct circles and related segments. Week 11 Example:  Suppose that a circle is divided by points A, B, C, and D into four congruent arcs.  What is the measure of each arc?  If these points are joined in order, what type of quadrilateral results? 6.5           6.6 Define and construct locus of points and concurrent lines of a triangle Week 12           Week 12 Example 1: In the figure, which of the points A, B, and C belong to "the locus of points in the plane that are at distance r from point P"?       Example 2: What is the general name of the point of concurrence for the three angle bisectors of a triangle? 7.1     7.2 Find the area and perimeter of various polygons Week 12     Week 12 Example 1: A rectangle's length is 6 cm, and its width is 9 cm.  Find the perimeter and the area of the rectangle.   Example 2: Using Heron's Formula, find the area of a triangle whose sides measure 13 in., 14 in., and 15 in.

 Chapter.Section Objective and Examples Material Covered 7.3 Define and use properties of regular polygons. Week 13 Example: Find the measure of the central angle of a regular polygon of five sides. 8.1       8.2 Find the area and volume of prisms and pyramids. Week 13       Week 14 Example 1: How many a) vertices, b) edges (lateral edges plus base edges) and c) faces (lateral faces plus bases) does a triangular prism have?   Example 2: In a pentagonal pyramid, suppose each base edge measures 9.2 cm and the apothem of the base measures 6.3 cm.  The altitude of the pyramid measures 14.6 cm.  Find the base area of the pyramid and the volume of the pyramid. 8.3 Find the area and volume of cones and cylinders Week 15 Example: The teepee has a circular floor with a radius equal to 6 ft and a height of 15 ft.  Find the volume of the enclosure. 8.4 Define properties of polyhedrons and use Euler's Formula. Week 15 Example: A regular polyhedron has 12 edges and 6 vertices.  a)   Use Euler's equation to find the number of faces. b)Use the results from part (a) to name the regular polyhedron.