GEOMETRY, PART 1

In this module, students gain a comprehension of the following:

• The foundations of Geometry – points, lines, and planes.
• The fundamentals of points, angles, lines, planes, segments, polygons, circles, and constructions.
• Measurements using perimeter, circumference, and area.
• The basic principles of reasoning including deductive and inductive reasoning.
• What conditional statements are, as well as converse, inverse, and contrapositive statements.
• To use logic and to develop algebraic, segment, and angle proofs.
• The nature of the angles formed when parallel lines are divided by a transversal.
• To prove lines are parallel, perpendicular, or neither, using information, like slope and a given point, to write an equation of a line.
• Identify three different forms of an equation of a line, including slope-intercept, point-slope, and standard form.
• The minimum requirements to determine whether or not two figures are congruent and congruency in other figures. Use SSS, SAS, AAS, ASA, and HL to prove triangles are congruent.
• Recognize and learn the key parts of isosceles and equilateral triangles. These properties will be used to prove corresponding parts of congruent triangles are congruent (CPCTC).
• The anatomy of triangles, including mid-segments, perpendicular bisectors, angle bisectors, medians, and altitudes of triangles.
• The concept of indirect proofs.
• The idea of inequalities in one triangle and inequalities in two triangles.
• The concept of the construction center of the triangle.
• The concept of ratio and proportion, using them to solve problems involving angle measures.
• Recognize the conditions that will make polygons similar, prove that triangles are similar using similarity theorems, and use the geometric mean to solve for the missing lengths of a triangle. Use proportionality to find the missing lengths in a triangle containing parallel lines.