Teaching Units 
Competencies and Objectives 
Fundamental concepts 
 Name and identify points, lines, planes, segments, rays, and angles.
 Determine midpoint and distance for points on a number line and
on the Cartesian Plane.
 Measure and classify angles.
 Identify and use special angle pairs.

Lines 
 Write the equation of a line given its graph, its slope and a point,
two points, or a table of values.
 Determine if lines are parallel, perpendicular, or neither using
slope.
 Write the equation of a line that is parallel or perpendicular to
a given line through a given point.

Logic 
 Make conjectures based upon inductive reasoning.
 Provide counterexamples.
 Create and interpret truth tables.
 Create and interpret Venn Diagrams.
 Identify the hypothesis and conclusion of a conditional statement.
 Create and determine the validity of the converse, inverse, and
contrapositie of conditional statements.
 Create and determine the validity of biconditional statements.
 Use the Law of Detachment and Law of Syllogism to determine the
validity of statements.

Introduction to proofs 
 Learn and use the Euclidean postulates.
 Construct algebraic proofs.
 Construct proofs about segments using the midpoint theorem and the
segment addition postulate.
 Construct proofs about angles using the definition of anlge bisector
and the angle addition postulate.
 Construct proofs about complementary and supplementary angles.
 Construct proofs involving right angles.

Proving lines are parallel or perpendicular 
 Identify corresponding, alternate interior, alternate exterior,
and consecutive interior angles.
 Prove angles are congruent when parallel lines are cut by a transversal.
 Prove lines are parallel using angle properties.
 Use properties of parallel lines cut by a transversal and algebra
to find angle measures.

Congruent and similar polygons 
 Solve proportions.
 Determine if two polygons are similar or congruent.
 Prove triangles are congruent or similar.
 Determine situations that create similar polygons.
 Use proportions to find missing lengths of polygons.
 Use proportional reasoning to determine perimeter and area of similar
figures.
 Use properties of isosceles and equilateral triangles to find angle
measures and side lengths.
 Use proportions to find angle measures when a line intersects a
triangle that is parallel to one of its sides.
 Use properties of altitudes, angle bisectors, and medians of triangles
to find angle measures and side lengths.

Properties of right triangles 
 Calculate the geometric mean.
 Use the geometric mean to determine missing lengths in right triangles
with an altitude drawn from the right angle.
 Use the Pythagorean Theorem and its converse to find side lengths
of right triangles, or determine if a triangle is a right triangle.
 Use properties of 306090 and 454590 triangles to find angle
measures and side lengths.
 Write ratios for lengths of sides of right triangles using sine,
cosine, and tangent.
 Use the inverse trigonometric functions to find angle measures.
 Use sine, cosine, and tangent to find missing side lengths in right
triangles.
 Use sine, cosine, and tangent to solve problems involving angles
of elevation and depression.
