Geometry Missouri Learning Standards*
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.
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))