Unit 1 Lesson 3 - In this video I review briefly what a conditional statement is, convers, inverse, contrapositive, counterexample, and biconditional. I then demonstrate proof by proving the Vertical Angle Theorem.
Unit 1 Lesson 4 - In this video I review the various angle pairs formed when a transversal line crosses two other lines. I review what types of angles are congruent and what types are parallel. We talk about the converse of each of these rules and then use them to prove a pair of lines parallel.
Unit 1 Lesson 5 - In this video I review what congruent triangles are. Then I review the postulate shortcuts for proving two triangles are congruent: SSS, SAS, ASA, AAS and HL. Finally, I prove two parts of two triangles are congruent by proving the triangles are congruent and then using CPCTC, corresponding parts.
Unit 2 Lesson 1 - In this video I define what a polygon is. Then we explore the relationship between the number of sides and the sum of all the interior angles. Next, we examine what an exterior angle is and discover what the sum of those exterior angles is for all polygons.
Unit 2 Lesson 2 - In this video I introduce the definition of a parallelogram. I then recount the five properties of parallelograms. Finally, I explain the 5 rules that can be used to prove a quadrilateral is a parallelogram, using the converse rules.
Unit 2 Lesson 3 - In this video I prove a given quadrilateral is a parallelogram.
Unit 2 Lesson 4 - In this video I define rhombus, rectangle and square, and briefly introduce some of their properties.
Unit 2 Lesson 5 - Here I outline what needs to be in place to prove a parallelogram is a rhombus, a rectangle, or a square.
Unit 2 Lesson 6 - The definitions and properties of a trapezoid, and isosceles trapezoid, and a kite are presented in this video.
Unit 2 Lesson 7 - Here we use the distance formula and slope formulas to identify a scalene acute triangle, and a rectangle given the coordinates of their vertices.
Unit 2 Lesson 8 - In this presentation we prove a given quadrilateral is a rhombus by using the distance formula to prove all the sides are congruent. We then prove it again by using the midpoint formula to show the diagonals bisect each other, and by using the slope formula to prove the diagonals are perpendicular. A quadrilateral with bisecting diagonals is a parallelogram, and a parallelogram with perpendicular diagonals is a rhombus.
Unit 2 Lesson 8 General Case - In this presentation we use coordinate geometry to prove the diagonals of all parallelograms bisect each other. We use Desmos to demonstrate how it represents all parallelograms.
Unit 3 Lesson 1 - In this video I review the various ways to wright ratios. I solve a basic ratio problem by writing and solving a proportion. Then demonstrate solving an algebraic proportion and ratio and perimeter problem.
Unit 3 Lesson 2 - In this video I explain what similar polygons are and contrast that with congruent polygons. We introduce dilation as a non-rigid transformation. We use proportions to solve for missing sides of similar polygons and also determine the scale factor of a dilation.
Unit 3 Lesson 3 - In this video I complete a proof that two triangles are congruent using the AA~ postulate.
Unit 3 Lesson 4 - In this video I explore what happens when a right triangle has an altitude drawn from its right angle, the three similar triangles that are formed and the relationship between them. I then solve for missing sides by solving proportions.
Unit 3 Lesson 5 - In this video I demonstrate in Geogebra the proportions formed by an angle bisector of a triangle and the proportions formed by a line parallel to a side of a triangle. I then use those proportions to solve for missing lengths.
Unit 4 Lesson 1 - In this video I introduce the Pythagorean Theorem and use it to solve for the missing side of a couple right triangles. I then use the converse of the Pythagorean Theorem to determine if a triangle with given sides is a right triangle.
Unit 4 Lesson 2 - In this video I demonstrate how to use the 45 45 90 reference triangle to solve for other 45 45 90 triangles and how to use the 30 60 90 reference triangle to solve for other 30 60 90 triangles.
Unit 4 Lesson 3 - In this video I explain how to solve right triangles using sine, cosine and tangent. First, I explain how to name the sides of a right triangle. Then I explain how to remember the three trig functions with SOH CAH TOA. Finally, I demonstrate how to use all of this to write and solve an equation for a given right triangle.
Unit 4 Lesson 4 - In this video I explain what is meant by angle of elevation and angle of depression using a scenario with a helicopter and an observer. I then answer questions about the scenario using the Pythagorean theorem and the tangent ratio, including using arctangent to find a missing angle.
Unit 4 Lesson 5 - In this video I present the two formulas, the law of sines and the law of cosines. I briefly explain when to use each and then demonstrate solving a non-right triangle in the ASA format.
Unit 4 Lesson 5 Part 2 - In this video I use the law of sines and the law of cosines to solve non-right triangles in the SAS and SSS arrangements.
Unit 5 Lesson 1 - In this video I explain what is meant by the area of a shape by using a grid to estimate the area of an irregular shape. I then demonstrate how to find the area of a rectangle, a parallelogram, and a triangle, noting how all three formulas are interconnected.
Unit 5 Lesson 2 - In this video I demonstrate how to find the area of a trapezoid and the area of a rhombus or kite using the appropriate formulas.
Unit 5 Lesson 3 - In this video I demonstrate how to use right triangle trigonometry to find the area of a regular pentagon, given its radius.
Unit 5 Lesson 4 - In this video I use squares to demonstrate the relationship between perimeters and areas of similar shapes. I then use that relationship to find a missing area for two similar shapes.
Unit 5 Lesson 5 - In this video I find the area of a triangle in which I know two sides and the angle between them, using A = 1/2 bh. But then I discover a shortcut in A = 1/2 ab sin C. I then use this new formula to find the area of a regular heptagon, given its radius.
Unit 5 Lesson 6 & 7 - In this video I write and solve proportions to find arc lengths and areas of sectors.
Unit 6 Lesson 1 - In this video I demonstrate what a geometric solid is by drawing a wire-frame cube. I define vertex, edge and face. I then present Euler's formula relating the number of vertices and faces to the number of edges and use it to find a missing value. Finally, I demonstrate various ways a cube might be sliced to produce faces of a variety of shapes.
Unit 6 Lesson 2 - In this video I define surface area and volume. I then explain the formula for the surface area of a prism and then compare it to the standard formula for the surface area of a rectangular prism. Finally, I explain the formula for the surface area of a cylinder.
Unit 6 Lesson 3 - In this video I explain and demonstrate the formulas for the surface area of a pyramid and the surface area of a cone.
Unit 6 Lesson 4 - In this video I demonstrate how to use the formula for the volume of a prism and the formula for the volume of a cylinder.
Unit 6 Lesson 5 - In this video I present the formulas for the volume of a pyramid and the volume of a cone. I then use them both.
Unit 6 Lesson 6 - In this video I demonstrate how to find the surface area and volume of a sphere of radius 4.
Unit 6 Lesson 7 - In this video I use cubes to explain what happens to ratios of length, area, and volume for similar solids. I then use these relationships to answer questions about how much paint to use and the weight of a scale model of a canoe.
Unit 7 Lesson 1 - In this video I define a tangent line as a line that touches a circle exactly once and explain why a tangent must be perpendicular to a radius at the point of tangency. I then solve a couple problems using this idea.
Unit 7 Lesson 2 - In this video I define chord and arc (major and minor), the measure of an arc and explain how congruent chords intercept congruent arcs and congruent arcs are intercepted by congruent chords. I then explore the perpendicular bisector of a chord and solve a problem based on the discovery that it creates two congruent right triangles.
Unit 7 Lesson 3 - In this video I define an inscribed angle and compare it to a central angle in Geogebra. I discover that an inscribed angle is always half the intercepted arc. I expand the rule to show that a tangent and a chord form an angle that is also half the intercepted arc. I also demonstrate that inscribed angles that intercept the same arc are always congruent.
Unit 7 Lesson 4 - In this video I use Geogebra to discover that chords intersect each other so the products of their parts are equal. I then use this rule to solve a problem.
Unit 7 Lesson 4 Part 2 - In this video I use Geogebra to discover that chords intersect each other so the vertical angles formed are the average of the intercepted arc. I then demonstrate how to use the formula for a given problem.
Unit 7 Lesson 4 Part 3 - In this video I use Geogebra to discover that secants that meet outside a circle create segments so that the outside * whole = outside * whole. I then use this relationship to solve a problem.
Unit 7 Lesson 4 Part 4 - In this video I use Geogebra to discover that the angle formed by secants outside a circle can be found by subtracting the intercepted arcs and dividing by 2. I then use this to answer a question.
Unit 7 Lesson 4 Part 5 - In this video I demonstrate how to solve a distance problem involving a tangent and a secant. I then find the angle formed by a tangent and a secant, and then the angle formed by two tangents.
Unit 7 Lesson 5 - In this video I use Desmos to present the formula for a circle. I then demonstrate how to write the equation of any given circle and how to graph a circle from its equation.
Unit 1 Lesson 4 - In this video I review the various angle pairs formed when a transversal line crosses two other lines. I review what types of angles are congruent and what types are parallel. We talk about the converse of each of these rules and then use them to prove a pair of lines parallel.
Unit 1 Lesson 5 - In this video I review what congruent triangles are. Then I review the postulate shortcuts for proving two triangles are congruent: SSS, SAS, ASA, AAS and HL. Finally, I prove two parts of two triangles are congruent by proving the triangles are congruent and then using CPCTC, corresponding parts.
Unit 2 Lesson 1 - In this video I define what a polygon is. Then we explore the relationship between the number of sides and the sum of all the interior angles. Next, we examine what an exterior angle is and discover what the sum of those exterior angles is for all polygons.
Unit 2 Lesson 2 - In this video I introduce the definition of a parallelogram. I then recount the five properties of parallelograms. Finally, I explain the 5 rules that can be used to prove a quadrilateral is a parallelogram, using the converse rules.
Unit 2 Lesson 3 - In this video I prove a given quadrilateral is a parallelogram.
Unit 2 Lesson 4 - In this video I define rhombus, rectangle and square, and briefly introduce some of their properties.
Unit 2 Lesson 5 - Here I outline what needs to be in place to prove a parallelogram is a rhombus, a rectangle, or a square.
Unit 2 Lesson 6 - The definitions and properties of a trapezoid, and isosceles trapezoid, and a kite are presented in this video.
Unit 2 Lesson 7 - Here we use the distance formula and slope formulas to identify a scalene acute triangle, and a rectangle given the coordinates of their vertices.
Unit 2 Lesson 8 - In this presentation we prove a given quadrilateral is a rhombus by using the distance formula to prove all the sides are congruent. We then prove it again by using the midpoint formula to show the diagonals bisect each other, and by using the slope formula to prove the diagonals are perpendicular. A quadrilateral with bisecting diagonals is a parallelogram, and a parallelogram with perpendicular diagonals is a rhombus.
Unit 2 Lesson 8 General Case - In this presentation we use coordinate geometry to prove the diagonals of all parallelograms bisect each other. We use Desmos to demonstrate how it represents all parallelograms.
Unit 3 Lesson 1 - In this video I review the various ways to wright ratios. I solve a basic ratio problem by writing and solving a proportion. Then demonstrate solving an algebraic proportion and ratio and perimeter problem.
Unit 3 Lesson 2 - In this video I explain what similar polygons are and contrast that with congruent polygons. We introduce dilation as a non-rigid transformation. We use proportions to solve for missing sides of similar polygons and also determine the scale factor of a dilation.
Unit 3 Lesson 3 - In this video I complete a proof that two triangles are congruent using the AA~ postulate.
Unit 3 Lesson 4 - In this video I explore what happens when a right triangle has an altitude drawn from its right angle, the three similar triangles that are formed and the relationship between them. I then solve for missing sides by solving proportions.
Unit 3 Lesson 5 - In this video I demonstrate in Geogebra the proportions formed by an angle bisector of a triangle and the proportions formed by a line parallel to a side of a triangle. I then use those proportions to solve for missing lengths.
Unit 4 Lesson 1 - In this video I introduce the Pythagorean Theorem and use it to solve for the missing side of a couple right triangles. I then use the converse of the Pythagorean Theorem to determine if a triangle with given sides is a right triangle.
Unit 4 Lesson 2 - In this video I demonstrate how to use the 45 45 90 reference triangle to solve for other 45 45 90 triangles and how to use the 30 60 90 reference triangle to solve for other 30 60 90 triangles.
Unit 4 Lesson 3 - In this video I explain how to solve right triangles using sine, cosine and tangent. First, I explain how to name the sides of a right triangle. Then I explain how to remember the three trig functions with SOH CAH TOA. Finally, I demonstrate how to use all of this to write and solve an equation for a given right triangle.
Unit 4 Lesson 4 - In this video I explain what is meant by angle of elevation and angle of depression using a scenario with a helicopter and an observer. I then answer questions about the scenario using the Pythagorean theorem and the tangent ratio, including using arctangent to find a missing angle.
Unit 4 Lesson 5 - In this video I present the two formulas, the law of sines and the law of cosines. I briefly explain when to use each and then demonstrate solving a non-right triangle in the ASA format.
Unit 4 Lesson 5 Part 2 - In this video I use the law of sines and the law of cosines to solve non-right triangles in the SAS and SSS arrangements.
Unit 5 Lesson 1 - In this video I explain what is meant by the area of a shape by using a grid to estimate the area of an irregular shape. I then demonstrate how to find the area of a rectangle, a parallelogram, and a triangle, noting how all three formulas are interconnected.
Unit 5 Lesson 2 - In this video I demonstrate how to find the area of a trapezoid and the area of a rhombus or kite using the appropriate formulas.
Unit 5 Lesson 3 - In this video I demonstrate how to use right triangle trigonometry to find the area of a regular pentagon, given its radius.
Unit 5 Lesson 4 - In this video I use squares to demonstrate the relationship between perimeters and areas of similar shapes. I then use that relationship to find a missing area for two similar shapes.
Unit 5 Lesson 5 - In this video I find the area of a triangle in which I know two sides and the angle between them, using A = 1/2 bh. But then I discover a shortcut in A = 1/2 ab sin C. I then use this new formula to find the area of a regular heptagon, given its radius.
Unit 5 Lesson 6 & 7 - In this video I write and solve proportions to find arc lengths and areas of sectors.
Unit 6 Lesson 1 - In this video I demonstrate what a geometric solid is by drawing a wire-frame cube. I define vertex, edge and face. I then present Euler's formula relating the number of vertices and faces to the number of edges and use it to find a missing value. Finally, I demonstrate various ways a cube might be sliced to produce faces of a variety of shapes.
Unit 6 Lesson 2 - In this video I define surface area and volume. I then explain the formula for the surface area of a prism and then compare it to the standard formula for the surface area of a rectangular prism. Finally, I explain the formula for the surface area of a cylinder.
Unit 6 Lesson 3 - In this video I explain and demonstrate the formulas for the surface area of a pyramid and the surface area of a cone.
Unit 6 Lesson 4 - In this video I demonstrate how to use the formula for the volume of a prism and the formula for the volume of a cylinder.
Unit 6 Lesson 5 - In this video I present the formulas for the volume of a pyramid and the volume of a cone. I then use them both.
Unit 6 Lesson 6 - In this video I demonstrate how to find the surface area and volume of a sphere of radius 4.
Unit 6 Lesson 7 - In this video I use cubes to explain what happens to ratios of length, area, and volume for similar solids. I then use these relationships to answer questions about how much paint to use and the weight of a scale model of a canoe.
Unit 7 Lesson 1 - In this video I define a tangent line as a line that touches a circle exactly once and explain why a tangent must be perpendicular to a radius at the point of tangency. I then solve a couple problems using this idea.
Unit 7 Lesson 2 - In this video I define chord and arc (major and minor), the measure of an arc and explain how congruent chords intercept congruent arcs and congruent arcs are intercepted by congruent chords. I then explore the perpendicular bisector of a chord and solve a problem based on the discovery that it creates two congruent right triangles.
Unit 7 Lesson 3 - In this video I define an inscribed angle and compare it to a central angle in Geogebra. I discover that an inscribed angle is always half the intercepted arc. I expand the rule to show that a tangent and a chord form an angle that is also half the intercepted arc. I also demonstrate that inscribed angles that intercept the same arc are always congruent.
Unit 7 Lesson 4 - In this video I use Geogebra to discover that chords intersect each other so the products of their parts are equal. I then use this rule to solve a problem.
Unit 7 Lesson 4 Part 2 - In this video I use Geogebra to discover that chords intersect each other so the vertical angles formed are the average of the intercepted arc. I then demonstrate how to use the formula for a given problem.
Unit 7 Lesson 4 Part 3 - In this video I use Geogebra to discover that secants that meet outside a circle create segments so that the outside * whole = outside * whole. I then use this relationship to solve a problem.
Unit 7 Lesson 4 Part 4 - In this video I use Geogebra to discover that the angle formed by secants outside a circle can be found by subtracting the intercepted arcs and dividing by 2. I then use this to answer a question.
Unit 7 Lesson 4 Part 5 - In this video I demonstrate how to solve a distance problem involving a tangent and a secant. I then find the angle formed by a tangent and a secant, and then the angle formed by two tangents.
Unit 7 Lesson 5 - In this video I use Desmos to present the formula for a circle. I then demonstrate how to write the equation of any given circle and how to graph a circle from its equation.