||Competencies and Objectives
- 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.
- 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
- Write the equation of a line that is parallel or perpendicular to
a given line through a given point.
- 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
- 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 30-60-90 and 45-45-90 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
- Use sine, cosine, and tangent to solve problems involving angles
of elevation and depression.