【Geometry】 Lesson 5: How to Partition a Line Segment to Find All Possible Coordinates of a Point?
[Learn Math by Example] Today I solve a math problem: how to partition a line segment to find all possible coordinates of a point. It belongs to Unit 1: partitioning formula problems. Please scroll down to see my whole course plan.
I am teaching math through examples. If you have any questions, please leave a comment.
Here is my course plan:
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Geometry with Trigonometry
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Unit 1:
Identify collinear and coplanar points
Distance formula problems
Midpoint formula and midsegment problems
Partitioning formula problems
Identify angle relationships (linear pair, vertical angles, complementary and supplementary angles)
Unit 2:
Two lines cut by a transversal (intersecting or parallel lines) and their angle relationship (alternate exterior and interior angles, consecutive interior angles, corresponding angles) problems
Proving two lines cut by a transversal are parallel with a two-column proof
Crook problems
Writing the equations of lines using slope intercept form
Unit 3:
Rotation, reflection, and translation problems (isometries) from equations and coordinate points
Graphing isometries problems
Glide reflection problems
Reflections in parallel lines theorem and reflections in intersecting lines theorem problems
Order and magnitude of regular polygon problems
Unit 4:
Identify if triangles are congruent given a set of properties (SSS, SAS, ASA, AAS)
Two-column proofs to identify if two triangles are congruent
Two-column proofs of congruent triangles with the application of CPCTC (corresponding parts of congruent triangles are congruent)
Classify a triangle by its angles and sides
Unit 5:
Find missing values in a triangle
Two-column proofs to prove the classification of triangles, their special line segments (altitude, angle bisector, median, perpendicular bisector), or the relationship between two line segments
Triangle angle-side relationship problems
Triangle inequality theorem problems
Find the equation of the altitude, median, or perpendicular bisector of a triangle
Special line segment word problems
Unit 6:
Find the image of coordinate points dilated with a scale factor
Determine if two triangles are similar (AA, SSS, SAS)
Similar triangle word problems
Triangle proportionality theorem problems
Unit 7:
Identify if a triangle is acute, right, or obtuse when given its 3 side lengths
Geometric mean (altitude) problems
Similar triangle problems (corresponding sides)
Special right triangle problems
Sin, cos, tan and inverse sin, inverse cos, inverse tan
Area of a triangle using sin
Law of sins and cosines
Unit 8:
Find the arc length, measure, and area of major arcs, minor arcs, and semicircles
Inscribed angle and quadrilateral problems
Circle chord theorems
Tangent of a circle problems
Graph and write the equation of a circle
Arc length (radians)
Unit 9:
Find the interior angle sum of a polygon and the measure of an interior or exterior angle of regular polygons
Identify if there is enough information to prove if a quadrilateral is a parallelogram
Prove if a quadrilateral is a parallelogram given its coordinate points
Find missing values or area of a quadrilateral
Find the area of a regular polygon with more than 4 sides using an apothem
Unit 10:
Find the volume of solids and composite solids
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【Geometry】 Lesson 5: How to Partition a Line Segment to Find All Possible Coordinates of a Point?