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) <ABC     b)<ACB

 

 

 

 

1.3

Understand geometrical foundations and fundamental postulates.

 

Week 1

 

Example:  Given M is the midpoint of the line AB, AM=2x + 1 and MB=3x -2, find x and AB.

 

 

1.4

 

 

 

Use and define angle types and relationships.

 

 

Week 2

 

 

 

 

Example 1: What type of angle is each of the following and what relationship, if any, exists between the two angles?      a)  37o       b)  143o

 

 

 

1.5

 

 

 

1.7

Define the parts of a direct proof and write a formal geometric proof.

 

 

Week 2

 

 

 

Week 3

 

Example 1: Given: D-E-F on line DF

Make a drawing and state a conclusion based on the Segment-Addition Postulate

 

Example 2: Complete a formal two-column direct proof of the following theorem, "If two lines intersect, the vertical angles formed are congruent."

 


 

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<A is greater than m<B, then AC will not equal BC.

b)If (x +2). (x - 3) = 0, then x = -2 or x = 3.

 

 

 

2.4

Classify triangles and construct different types of triangles.

 

 

 

Week 5

 

Example: Draw, if possible, an

a)    isosceles obtuse triangle.

b)   equilateral right triangle.

 

 

 

2.5

Define properties of convex polygons and construct convex polygons.

 

 

 

Week 5

 

Example:  The face of a clock has the shape of a regular polygon with 12 sides.  What is the measure of the interior and exterior angle formed by two consecutive sides?

 


 

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: <MPN and <MPQ are right angles and P is the midpoint of line NQ.  Prove: <N is congruent to <Q.

 

 

3.3

Define and use isosceles triangles.

 

 

Week 7

 

Example: Find the measure of <1 and <2 if the measure of <3 is 68o

 

 

 

 

 

 

3.5

Define and use triangle inequality theorems.

Week 7

 

Example: If possible, draw a triangle whose

(a)    angles measure 100o, 100o, and 60o.

(b)   sides measure 8, 9, and 10.

 


 

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<A = 2x + 3 and m<B = 3x - 23, find the measure of each angle of the parallelogram ABCD shown below.

 

 

 

Example 2: A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end-to-end.

(a)    If these are joined at the ends to form a quadrilateral that has the 8-ft pieces connected in order, what type of quadrilateral is formed?

(b)   If these are joined at the ends to form a quadrilateral that has the 4-ft and 8-ft pieces alternating, what type of quadrilateral is formed?

 

 

 

4.3

 

 

4.4

Define and use the properties of various quadrilaterals.

 

 

Week 9

 

 

Week 9

 

Example 1: Given rectangle ABCD, with AB = 2x + 7, BC = 3x + 4 and CD = 3x + 2, find x and DA.

 

Example 2: The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340 miles on the north, 515 miles on the east, 435 miles on the south, and 225 miles on the west.  If A and B are points located midway across the north and south boundaries, what is the approximate distance directly from point A to point B?

 

 

5.1

Understand and use ratios, rates, and proportions in geometry.

 

 

Week 10

 

Example: Assume that AD is the geometric mean of BD and DC in triangle ABC shown in the accompanying drawing.  Find AD if BD = 6 and DC = 8.

 

 

 


 

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.