Geometry

Congruence

Video:  Angle basics (6:48 mins)

Video:  Measuring angles in degrees (8:22 mins)

Video:  Measuring angles using a protractor (3:22 mins)

Video:  Parallel and perpendicular lines intro (2:07 mins)

Video:  Angles formed by parallel lines and transversals  (7:07 mins)

Video:  Identifying parallel and perpendicular lines (3:34 mins)

Video:  Introduction to transformations (7:22 mins)

Video:  Another example of rigid transformations for congruence (5:01 mins)

Video:  Drawing image of translation (1:54 mins) 

Video:  Translation example (1:36 mins)

Video:  Matrix transformation on triangle  (7:14 mins)

Video:  Matrix equations and systems (9:53 mins)

Video:  Transforming a quadrilateral (6:07 mins)

Video:  Rotating polygons 180 degrees about their center (4:07 mins)

Video:  Rotating about arbitrary point (10:31 mins)

Video:  Points after rotation (8:12 mins)

Video:  Points on line of reflection (5:40 mins)

Video:  Reflecting segments over line (7:18 mins)

Video:  Reflecting line across another line example (1:15 mins) 

Video:  Axis of symmetry (2:46 mins) 

Video:  Constructing a shape by reflecting over 2 lines  (7:19 mins) 

Video:  Two column proof showing segments are perpendicular (11:05 mins)

Video:  Review of triangle properties (9:56 mins)

Video:  Line and angle proofs exercise (8:44 mins)

Video:  Congruent triangle proof example (5:45 mins)

Video:  Congruent triangles and SSS (11:28 mins)

Video:  Congruent triangle example 2 (12:13 mins)

Video:  Other triangle congruence postulates (13:27 mins)

Video:  Fill-in-the-blank triangle proofs example 1 (9:41 mins)

Video:  Fill-in-the-blank triangle proofs example 2 (6:38 mins)

Video:  Congruence and similarity — Basic example (4:18 mins)

Video:  Congruence and similarity — Harder example (3:17 mins)

Video:  CA Geometry: More on congruent and similar triangles (11:11 mins)

Video:  Constructing a tangent line using compass and straightedge (5:49 mins)

Video:  Another example using compass and straightedge for tangent line (5.34 mins)

 

  • Define angle, circle, perpendicular line, parallel line, segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.

  • Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.

  • Describe the rotational symmetry and lines of symmetry of two-dimensional figures.

  • Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

  • Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.

  • Develop the definition of congruence in terms of rigid motions.

  • Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.

  • Prove theorems about lines and angles.

  • Prove theorems about triangles.

  • Prove theorems about polygons.

  • Construct geometric figures using various tools and methods.

 

Similarity, Right Triangles, & Trigonometry

Video:  Constructing quadrilateral based on symmetry (3:06 mins)

Video:  Scaling down a triangle by half (2:25 mins)

Video:  Similar triangle basics (9:16 mins)

Video:  Testing similarity through transformations (2:10 mins)

Video:  Similarity postulates (12:13 mins)

Video:  Similarity example where same side plays different roles | (6:04 mins)

Video:  Triangle similarity in pool (6:48 mins)

Video:  Challenging similarity problem (9:52 mins)

Video:  Finding area using similarity and congruence (10:06 mins)

Video:  The Pythagorean theorem intro (10:45 mins) 

Video:  45-45-90 triangles (9:30 mins)

Video:  Intro to 30-60-90 triangles (9:39 mins)

Video:  30-60-90 triangle side ratios proof (6:59 mins)

Video:  30-60-90 triangle example problem (6:39 mins)

Video:  Basic trigonometry (9:16 mins)

Video:  Basic trigonometry II (12:10 mins)

Video:  Matching ratios to trig functions (6:56 mins)

Video:  Pythagorean trig identity from soh cah toa  (4:15 mins)

Video:  Example: Trig to solve the sides and angles of a right triangle (7:03 mins)

Video:  Example: Using trig to solve for missing information (6:11 mins)

 

 

 

  • Construct and analyze scale changes of geometric figures.

  • Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.

  • Use the properties of similarity transformations to establish the AA criterion for two triangles to similar.

  • Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

  • Understand that side ratios in right triangles define the trigonometric ratios for acute angles.

  • Explain and use the relationship between the sine and cosine of complementary angles.

  • Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

  • Derive the formula A = 1/2ab sin(C) for the area of a triangle.

 

Circles

Video:  Circles: radius, diameter, circumference and Pi (11:04 mins)

Video:  Labeling parts of a circle (2:00 mins)

Video:  Inscribed angle theorem proof (14:16 mins)

Video:  Inscribed quadrilaterals proof (3:55 mins)

Video:  Solving inscribed quadrilaterals (4:57 mins)

Video:  Inscribed shapes: find inscribed angle (2:09 mins)

Video:  Constructing square inscribed in circle (2:46 mins)

Video:  Length of an arc that subtends a central angle (4:57 mins)

Video:  Angle measurement and circle arcs (7:36 mins)

Video:  Finding arc measures with equations (6:57 mins)

Video:  Area of a sector given a central angle (2:25 mins)

  • Prove that all circles are similar using similarity transformations.

  • Identify and describe relationships among inscribed angles, radii and chords of circles.

  • Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

  • Derived the formula for the length of an arc of a circle.

  • Derive the formula for the area of a sector of a circle.

 

Exploring Geometric Properties with Equations

Video:  Introduction to conic sections | Conic sections (10:57 mins)

Video:  Conic Sections: Intro to Circles (9:03 mins)

Video:  Equation for a circle using the Pythagorean Theorem (6:18 mins)

Video:  Radius and center for a circle equation in standard form (3:50 mins)

Video:  Equation for parabola from focus and directrix (9:47 mins)

 

  • Derive the equation of a circle.

  • Derive the equation of a parabola given a focus and directrix.

  • Use coordinates to prove geometric theorems algebraically.

  • Prove the slope criteria for parallel and perpendicular lines and uses them to solve problems.

  • Find the point on a directed lined segment between two given points that partitions the segment in a given ratio.

  • Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

 

Geometric Measurement & Dimension

Video:  Circumference of a circle (1:52 mins)

Video:  Area of a circle (6:44 mins)

Video:  Cylinder volume and surface area (8:06 mins)

Video:  Slice a rectangular pyramid (3:29 mins)

Video:  Volume of a cone (5:43 mins)

Video:  Volume of a Composite Shape (7:12 mins)

 

  • Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.

  • Use volume formula for cylinders, pyramids, cones, spheres and composite figures to solve problems.

  • Identify the shapes of two-dimensional cross-sections of three-dimensional objects.

 

Modeling with Geometry

  • Use geometric shapes, their measures and their properties to describe objects.

  • Apply concepts of density based on area and volume in modeling situations.

  • Apply geometric methods to solve design mathematical modeling problems.

 

Conditional Probability and Rules of Probability

Video:  Calculating conditional probability (6:42 mins)

Video:  Addition rule for probability (10:42 mins)

Video:  Introduction to combinations (6:17 mins)

Video:  Combination formula (11:16 mins)

Video:  Permutation formula (7:34 mins)

 

  • Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.

  • Understand the definition of independent events and use it to solve problems.

  • Calculate conditional probability of events.

  • Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified.  Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

  • Recognize and explain the concepts of conditional probability and independence in a context.

  • Apply and interpret the Addition Rule for calculating probabilities.

  • Apply and interpret the general Multiplication Rule in a uniform probability model.

  • Use permutations and combinations to solve problems.

* Sources:  dese.mo.gov (Course Level Expectations (CLEs))