Geometry

Geometry focuses on the use of structured logic to study concepts relating to angles, lines, congruence and similarity, polygons, and three-dimensional figures. Students apply logic and reason to prove geometric theorems.  Pathfinder Tech follows the Model Geometry Traditional Pathway from the Massachusetts Mathematics Curriculum Frameworks which emphasizes that Geometry focus on the following 6 areas:

(1)  establish criteria for congruence of triangles based on rigid motions;

(2)  establish criteria for similarity of triangles based on dilation and proportional reasoning;

(3)  informally develop explanations of circumference, area, and volume formulas;

(4)  apply the Pythagorean Theorem to the coordinate plane;

(5)  prove basic geometric theorems;

(6)  extend work with probability.

(Click here to read more about the Massachusetts Mathematics Curriculum Frameworks.)

Learning Targets Students will be able to...

• Graph and read points in the coordinate plane.

• Identify quadrants in the coordinate plane.

• Find distance and midpoint between two points. (using formulas & graphs)

• Identify transformations in the coordinate plane. (translations, reflections, rotations, and dilations)

• Graph transformations in the coordinate plane. (translations, reflections, rotations, and dilations)

Learning Targets Students will be able to...

• Find the slope of a line (graphically and from formula).

• Use slope to determine if lines are parallel, perpendicular, or neither.

• Graph equations of lines given an equation in slope-intercept form.

• Write equations of lines in slope-intercept form given a graph.

• Identify solutions of systems of linear equations in two variables.

• Solve systems of linear equations in two variables by graphing.

• Solve systems of linear equations in two variables algebraically (substitution and elimination).

• Graph and solve linear inequalities in two variables.

• Graph and solve systems of linear inequalities in two variables.

• Model real-world situations using systems.

Learning Targets Students will be able to...

• Identify, name, and draw basic geometric figures (points, lines, segments, rays, and planes).

• Apply theorems about segment and midpoint to find measurements.

• Apply theorems about segment and midpoint to write and solve algebraic equations.

• Name and classify angles.

• Apply theorems about angles and bisectors to find measurements.

• Apply theorems about angles and bisectors to write and solve algebraic equations.

• Identify angle pairs (linear, adjacent, vertical, complementary, and supplementary).

• Apply theorems about angle pairs to find measurements.

• Apply theorems about angle pairs to write and solve algebraic equations.

• Identify types of lines (parallel, perpendicular, intersecting, skew).

• Identify the angles formed by two lines and a transversal.

• Apply theorems about the angles formed by parallel lines and a transversal to find measurements.

• Apply theorems about the angles formed by parallel lines and a transversal to write and solve algebraic equations.

Learning Targets Students will be able to...

• Classify triangles by their angle measures and side lengths.

• Use triangle classification to find angle measures and side length.

• Find measures of interior and exterior angles of triangles.

• Apply properties of isosceles and equilateral triangles.

• Use CPCTC to prove parts of triangles are congruent.

• Apply properties of congruent figures to solve problems.

• Prove triangles congruent by using the definition of congruence.

• Apply SSS, SAS, ASA, AAS, and HL to construct triangles and to solve problems.

• Write and simplify ratios.

• Solve algebraic proportions.

• Apply properties of similar figures to solve problems.

• Use proportions to solve problems involving parallel lines in a triangle.

Learning Targets Students will be able to...

• Apply the Pythagorean Theorem to find a side length in a right triangle.

• Justify and apply properties of 45-45-90 triangles.

• Justify and apply properties of 30-60-90 triangles.

• Find cosine, sine, and tangent of an acute angle.

• Apply trigonometric ratios to find side lengths in right triangles and to solve real-world problems.

• Apply trigonometric ratios to find angle measures in right triangles and to solve real-world problems.

Learning Targets Students will be able to...

• Classify polygons based on their sides and angles.

• Find and use the measures of interior and exterior angles of polygons.

• Apply properties of parallelograms (including rectangles, rhombuses, and squares).

• Apply properties of quadrilaterals (including kites and trapezoids).

• Apply formulas for perimeter, area, and circumference.

Learning Targets Students will be able to...

• Identify parts of circles (center, diameter, radius, circumference, arc, secant, tangent, chord, central angle, inscribed angle)

• Apply properties of arcs, chords, and inscribed angles.

• Solve problems involving parts of circles.

• Apply formulas for area, and circumference.

• Find the area of sectors.

• Use composite figures to calculate or estimate the areas of irregular shapes.

• Find the area of sectors.

Learning Targets Students will be able to...

• Classify three-dimensional figures according to their properties (prism, cylinder, pyramid, cone, sphere). 

• Use nets and cross sections to analyze three-dimensional figures.

• Apply the formulas for the surface area of three-dimensional polyhedrons.

• Apply the formulas for the volume of three-dimensional polyhedrons.

Learning Targets Students will be able to...

• Simplify and evaluate expressions containing exponents.

• Simplify and evaluate expressions containing square roots.

• Classify numbers within the real number system.