Course title
422Pre-requisite
Intermediate Algebra 1-2 or Algebra 1-2Course description
422 Geometry Essentials 1-2
This is a course in Euclidean Geometry. Topics include
transformations; congruence; similarity; parallel lines;
coordinate geometry; circles; perimeter; area; surface area;
volume; geometric proofs; and a review of Algebra I concepts.
Geometry students will understand the following big idea
and essential question: Geometry concepts are represented
throughout the real world. Where are the geometric concepts
applied in the world outside the classroom? Students receive
support for; and focus on; learning the Arizona Common Core
Mathematical Standards.
Essentials of Geometry
Lesson Lesson Objectives NCTM Standards 2000
Quarter 1 1.1 Identify patterns and use inductive reasoning. 1; 2; 3; 4; 6; 7; 8; 9; 10
1.2 Identify and draw models of points; lines; and planes; and determine their characteristics 2; 3; 8; 9
1.3 Identify and use postulates about points; lines; and planes 3; 6; 7; 8; 9; 10
1.4 Write statements in if-then form and write the converses of the statements 5; 6; 7; 8; 9
1.5 Use geometric tools 2; 3; 4; 6; 7; 8; 9
1.6 Use a four-step plan to solve problems that involve the perimeters and areas of rectangles and parallelograms 1; 2; 3; 4; 6; 7; 8; 9; 10
2.1 Find the distance between two points on a number line 1; 2; 4; 6; 7; 8; 9; 10
2.2 Apply the properties of real numbers to the measure of segments 1; 2; 3; 4; 6; 8; 9
2.3 Identify conguent segments and find the midpoints of segments 1; 2; 3; 4; 6; 7; 8; 9; 10
2.4 Name and graph ordered pairs on a coordinate plane. 1; 2; 3; 6; 8; 9
2.5 Find the coordinates of the midpoint of a segment 1; 3; 4; 6; 8; 9
3.1 Name and identify parts of an angle 1; 3; 4; 6; 8; 9; 10
3.2 Measure; draw; and classify angles 1; 2; 3; 4; 6; 8; 9; 10
3.3 Find the measure of an angle and the bisector of an angle 1; 2; 3; 4; 6; 8; 9
3.4 Identify and use adjacent angles and linear pairs of angles 1; 3; 4; 6; 8; 9; 10
3.5 Identify and use complementary and supplementary angles 1; 2; 3; 4; 6; 8; 9; 10
3.6 Identify and use congruent and vertical angles 1; 3; 4; 6; 7; 8; 9
3.7 Identify; use properties of; and construct perpendicular lines and segments 1; 2; 3; 4; 6; 7; 8; 9
Quarter 2 4.1 Describe relationships among lines; parts of lines; and planes. 3; 4; 6; 8; 9
4.2 Identify the relationships among pairs of interior and exterior angles formed by two parallel lines and a transversal 1; 2; 3; 4; 6; 7; 8
4.3 Identify the relationships among pairs of corresponding angles formed by two parallel lines and a transversal 3; 4; 8
4.4 Identify conditions that produce parallel lines and construct parallel lines 1; 2; 3; 4; 6; 7; 8; 9
4.5 Find the slopes of lines and use slope to identify parallel and perpendicular lines 1; 2; 3; 4; 5; 6; 7; 8; 9; 10
4.6 Write and graph equations of lines 1; 2; 3; 4; 6; 7; 8; 9; 10
5.1 Identify the parts of triangles and classify triangles by their parts 1; 2; 3; 4; 6; 7; 8; 9
5.2 Use the Angle Sum Theorem 1; 2; 3; 4; 6; 7; 8; 9; 10
5.3 Identify translations; reflections; and rotations and their corresponding parts 1; 3; 4; 6; 7; 8
5.4 Names and label corresponding parts of congruent triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
5.5 Use the SSS and SAS tests for congruence 3; 4; 6; 7; 8; 9
5.6 Use the ASA and AAS tests for congruence 3; 4; 6; 7; 8; 9
6.1 Identify and construct medians in triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
6.2 Identify and construct altitudes and perpendicular bisectors in triangles 3; 4; 6; 7; 8
6.3 Identify and use angle sbisectors in triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
6.4 Identify and use properties of isosceles triangles 1; 2; 3; 4; 6; 7; 8; 9
6.5 Use tests for congruence of right triangles 1; 2; 3; 4; 6; 7; 8; 9
6.6 Use the Pythagorean Theorem and its converse 1; 2; 3; 4; 5; 6; 7; 8; 9; 10
6.7 Find the distance between two points on the coordinate plane. 1; 2; 3; 4; 5; 6; 7; 8; 9; 10
Quarter 3 7.1 Apply inequalities to segment and angle measures 1; 2; 3; 4; 6; 7; 8; 9; 10
7.2 Identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem 1; 2; 3; 4; 6; 7; 8; 9; 10
7.3 Identify the relationships between the sides and angles of a triangle 1; 2; 3; 4; 6; 7; 8; 9; 10
7.4 Identify and use the Triangle Inequality Theorem 1; 2; 3; 4; 6; 7; 8; 9; 10
8.1 Identify parts of quadrilaterals and find the sum of the measures of the interior angles of a quadrilateral 1; 2; 3; 4; 6; 7; 8; 9
8.2 Identify and use the properties of paralleograms 1; 2; 3; 4; 6; 7; 8
8.3 Identify and use tests to show that a quadrilateral is a parallelogram 1; 2; 3; 4; 6; 7; 8; 9
8.4 Identify and use the proerpties of rectangles; rhombi; and squares 1; 2; 3; 4; 6; 8; 9; 10
8.5 Identify and use the properties of trapezoids and isosceles trapezoids 1; 2; 3; 4; 6; 7; 8; 9; 10
9.1 Use ratios and proportions to solve problems 1; 2; 3; 4; 6; 7; 8; 9; 10
9.2 Identify similar polygons 1; 2; 3; 4; 6; 7; 8; 9; 10
9.3 Use AA; SSS; and SAS similarity tests for triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
9.4 Identify and use the relationships between proportional parts of triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
9.5 Use proportions to determine whether lines are parallel to sides of triangles 1; 2; 3; 4; 6; 7; 8; 9
9.6 Identify and use the relathionshios between parallel lines and proportional parts 1; 2; 3; 4; 6; 7; 8; 9; 10
9.7 Identify and use the relationships of similar triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
Quarter 4 10.1 Name polygons according to the number of sides and angles 1; 2; 3; 4; 6; 7; 8; 9
10.2 Find measures of interior and exterior angles of polygons 1; 2; 3; 4; 6; 7; 8
10.3 Estimate the areas of polygons 3; 4; 6; 7; 8
10.4 Find the areas of triangles and trapezoids 1; 2; 3; 4; 6; 7; 8; 9; 10
10.5 Find the areas of regular polygons 1; 2; 3; 4; 6; 7; 8
10.6 Identify figures with line symmetry and rotational symmetry 1; 2; 3; 4; 6; 7; 8; 9; 10
10.7 Identify tessellations and create them by using transformations 1; 2; 3; 4; 6; 7; 8; 9; 10
11.1 Identify and use parts of circles 1; 2; 3; 4; 6; 7; 8; 9
11.2 Identify major arcs; minor arcs; and semicircles and find the measures of arcs and central angles 3; 4; 6; 7; 8
11.3 Identify and use the relationships among arcs; chords; and diameters 1; 2; 3; 4; 6; 7; 8; 9
11.4 Inscribe regular polygons in circles and explore the relationship between the length of a chord and its distance from the center of the circle 1; 2; 3; 4; 6; 7; 8; 9; 10
11.5 Solve problems involving circumferences of circles 1; 2; 3; 4; 6; 7
11.6 Solve problems involving areas and sectors of circles 1; 2; 3; 4; 6; 7; 8; 9; 10
12.1 Identify solid figures 3; 4; 6; 7; 8
12.2 Find the lateral areas and surfance areas of prisms and cylinders 1; 2; 3; 4; 6; 7; 8; 9
12.3 Find the volumes of prisms and cylinders 1; 2; 3; 6; 7; 8; 9; 10
12.4 Find the lateral areas and surgace areas of regular pyramids and cones 1; 2; 3; 4; 6; 7; 8; 9; 10
12.5 Find the volumes of pyramids and cones 1; 2; 3; 4; 6; 7; 8; 9; 10
12.6 Find the surface areas and volumes of spheres 1; 2; 3; 4; 6; 7; 8; 9; 10
12.7 Identify and use the relationships between similar solid figures 1; 2; 3; 4; 6; 7; 8; 9; 10
13.1 Multiply; divide; and simplify radical expressions 1; 2; 3; 4; 6; 7; 8; 9; 10
13.2 Use the properties of 45-45-90 triangles 1; 2; 3; 4; 6; 7; 8; 9
13.3 Use the properties of 30-60-90 triangles 1; 2; 3; 4; 6; 7; 8; 9; 10
13.4 Use the tangent ratio to solve problems 1; 2; 3; 4; 6; 7; 8; 9; 10
13.5 Use the sine and cosine ratios to solve problems 1; 2; 3; 4; 6; 7; 8; 9; 10
14.1 Identify and use properties of inscribed angles 1; 2; 3; 4; 6; 7; 8
14.2 Identify and apply properties of tangents to circles 1; 2; 3; 4; 6; 7; 8; 9
14.3 Find measures of arcs and angles formed by secants 1; 2; 3; 4; 6; 7; 8; 9
14.4 Find measures of arcs and angles formed by secants and tangents 1; 2; 3; 4; 6; 7; 8; 9; 10
14.5 Find measures of chords; secants; and tangents 1; 2; 3; 4; 6; 7; 8; 9; 10
14.6 Write equations of circles using the center and the radius 1; 2; 3; 4; 6; 7; 8; 9; 10
15.1 Find the truth values of simple and compoound statements 1; 2; 3; 6; 7; 8
15.2 Use the Law of Detachment and the Law of Syllogism in deductive reasoning 1; 2; 3; 4; 6; 7; 8
15.3 Use paragraph proofs to prove theorems 1; 2; 3; 6; 7; 8
15.4 Use properties of equality in algebraic and geometric proofs 1; 2; 3; 4; 6; 7; 8; 9
15.5 Use two-column proofs to prove theorems 1; 2; 3; 4; 6; 7; 8; 9
15.6 Use coordinate proofs to prove theorems 1; 2; 3; 4; 6; 7; 8; 9
16.1 Solve systems of equations by graphing 1; 2; 3; 4; 6; 7; 8; 9
16.2 Solve systems of equations by using the substitution or elimination method 1; 2; 3; 4; 6; 7; 8
16.3 Investigate and draw translations on a coordinate plane 1; 2; 3; 4; 6; 7; 8; 9
16.4 Investigate and draw reflections on a coordinate plane 1; 2; 3; 4; 6; 7; 8; 9
16.5 Investigate and draw rotations on a coordinate plane 1; 2; 3; 4; 6; 7; 8; 9
16.6 Investigate and draw dilations on a coordinate plane 1; 2; 3; 4; 6; 7; 8; 9
*Key to NCTM standards 2000
1 - number and operations
2 - algebra
3 - geometry
4 - measurement
5 - data analysis and probability
6 - problem solving
7 - reasoning and proof
8 - communications
9 - connections
10 - representation
School Country
United StatesSchool state
ArizonaSchool city
PhoenixSchool Address
15002 N 32nd Street Phoenix, AZSchool zip code
85050Date submitted
Approved
YesApproved competency code
- MTH2
- 4 years of Math