** **

An explanation of the rules we would use for Reflections in the coordinate plane. What to do to reflect ordered pairs across the x-axis, the y-axis, or a line in which y = x as the lines of reflection. What it means to have a line in which y = x.

Geometry 9.1a, Reflections & isometry

https://youtu.be/VTqV0jYqYH4

High School Geometry Playlist

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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November 2, 2018. The girls are rolling around and play fighting again.

A typical morning with two silly dogs.

An explanation of how a reflection is a transformation across a line called the "Line of Reflection". How the line of reflection is the perpendicular bisector of each segment joining each point and its image. An isometry is a transformation that doesn't change the shape or size of a figure, such as a reflection, translation, or rotation. We identify reflections and we demonstrate a reflection using tissue paper. We draw a reflection of a quadrilateral using perpendicular lines from each vertex of the pre-image. We discuss reflection notation and how to read and write it with tick marks. We find the shortest trail possible from two campsites to a river using a reflection.

High School Geometry Playlist

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An introduction and explanation of vectors, and component form as the horizontal and vertical change from the initial point to the terminal point. We see how to write vectors in component form, discuss the magnitude of a vector as its length, we use the distance formula to find the magnitude of a vector, the direction of a vector is the angle that it makes with a horizontal line, how the direction of a vector can be given as a bearing that is relative to compass directions, zero vector, finding the direction of a vector as an inverse tangent, and vector notation that we will be using.

High School Geometry Playlist

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of when we can use the Law of Cosines to solve a triangle (when we have SAS or SSS). Using the Law of Cosines and an inverse cosine function to find a missing side length, or find a missing angle measure, and another formula we can use to find the measure of an angle if we know three side lengths.

Geometry 8.5a, Find Trig ratios for obtuse angles with a scientific calculator

https://youtu.be/Bfqh0Brnhz4

Geometry 8.5b, Law of Sines

https://youtu.be/xZrn6toZN3E

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how we can solve any triangle by calculating trigonometric ratios for angles up to 180 degrees. We discuss the Law of Sines and how we can use it to solve a triangle if we're given the angle measures and any side lengths, or two side lengths and a non-included angle measure. Using the cross products property to find a side length, or using the inverse sine function to find an angle measure. How the Law of Sines can be derived from the formula for the area of a triangle. Why the trig ratios of some angles are negative.

Geometry 8.5a, Find Trig ratios for obtuse angles with a scientific calculator

https://youtu.be/qkEZvL-jf5k

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An explanation of how to find trig ratios for obtuse angles with a scientific calculator. Which order to push the keys to find a sine, cosine, or tangent ratio for an obtuse angle.

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of an angle of elevation and an angle of depression. How they are formed using a horizontal line and a line of sight. We classify angles of elevation and depression, we find Distance by using an angle of elevation, then we find Distance by using an angle of depression. We see how the Alternate Interior Angles theorem can help us find and angle measure. We write a tangent ratio and solve for the length of one side of a right triangle as the distance from one point to another. At the end, I explain why it's better to round off amounts after adding or subtracting to be more accurate.

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of what it means to "Solve a Triangle", solving a right triangle from two sides and an acute angle. Finding unknown measures by using the Pythagorean Theorem, the inverse tangent, or complementary angles. We discuss the inverse sine of x is the angle whose sine equals x, the inverse cosine of x is the angle whose cosine equals x, the inverse tangent of x is the angle whose tangent equals x. We solve a right triangle in the coordinate plane. We find the angle that a hill makes with a horizontal line from its percent grade, in San Francisco.

Geometry 8.3a, Identify & Calculate Angle Measures from Trig Ratios

https://youtu.be/rBlW9zZrt-s

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November 26, 2018. The weather forecast is 9 to 12 inches of snow, but I don't think it will get that deep. I have already shoveled once, an hour ago, and the snow is piling up again. It actually feels like tiny ice pellets instead of fluffy snow, very wet and heavy!

An explanation of how we can identify and calculate angle measures from a trigonometric ratio. How we can use an inverse trig function to find an angle measure when the ratio of side lengths is known in a right triangle. Using a scientific calculator to find an angle measure to the nearest degree. Using the "Real Calc scientific calculator" app to find angle measures by using inverse trig functions.

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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November 21, 2018. Babysitting my 18 month old granddaughter. Lola flinging her stuffed bunny in the background. (Notice I have to block access to the dry erase board because my granddaughter likes to erase my work!)

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An explanation of how we can find the sine and cosine of acute angles in a right triangle by using the complement of that angle. The trigonometric function of the complement of an angle is called a cofunction, and the sines and cosines are cofunctions of each other. We write sine and cosine terms, and cosine and sine terms. We find unknown angle measures that will satisfy an algebraic equation for the variable x.

Geometry 8.2a, Trigonometric Ratios, introducing Sine, Cosine, Tangent

https://youtu.be/z_r8PGb-NqM

Geometry 8.2b, Finding & Calculating Trigonometric Ratios

https://youtu.be/R8NshjG6guo

Geometry 8.2c, Calculating Trig Ratios with a Trig Table

https://youtu.be/NobppRSsNus

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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We use a trig table (trigonometric table) to find a missing length of a right triangle. We solve a problem from the previous video (when we used a calculator) about a wheelchair ramp by using a trig table. We use the mnemonic soh-cah-toa to help us decide which legs to use. We round a decimal to the closest degree on the trig table. We also find sinA to the closest degree, find the difference between the two options, then decide which one to use. How finding the sine will help us find the cosine.

Geometry 8.2a, Trigonometric Ratios, introducing Sine, Cosine, Tangent

https://youtu.be/z_r8PGb-NqM

Geometry 8.2b, Finding & Calculating Trigonometric Ratios

https://youtu.be/R8NshjG6guo

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how we can find trigonometric ratios and write them as a fraction, using what we have learned about the sine, cosine, and tangent of a right triangle in video 8.2a. We learn the mnemonic soh-cah-toa and use it to write the trigonometric ratio of a given right triangle as a fraction and decimal, rounded to the nearest hundredth. We find the trigonometric ratio of a special right triangle of 30°-60°-90°, and we learn to use our calculator to find trigonometric ratios and round them to the nearest hundredth. We find a length using a tangent ratio, sine ratio, and cosine ratio. We find the length of a wheelchair ramp along the ground with a given segment length and angle measure.

Geometry 8.2a, Trigonometric Ratios, introducing Sine, Cosine, Tangent

https://youtu.be/z_r8PGb-NqM

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An introduction and explanation of trigonometric ratios as the ratio of two sides of a right triangle. We discuss sine, cosine, and tangent. An explanation of sinA, sinB, cosA, cosB, tanA, tanB, how to find opposite legs, and how to find adjacent legs. An explanation of the word tangent and it's two meanings in geometry. How the six parts of a right triangle (3 sides and 3 angles) can be paired into three different pairings. How the six different answers we get, dividing those pairings, are the six trigonometric functions of sine, cosine, tangent, cotangent, secant, and cosecant.

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how the altitude drawn from the vertex of a right triangle to the hypotenuse forms two right triangles. A theorem (8.1.1) about an altitude drawn to the hypotenuse of a right triangle will form two similar triangles, and a we do a proof of that theorem. We discuss the geometric mean of two positive numbers is the positive square root of their product. We find the geometric mean of a pair of numbers and write them in simplest radical form. We use our theorem to write proportions comparing the side lengths of right triangles formed by the altitude to the hypotenuse. Geometric Means Corollaries 8.1.2 and 8.1.3 are used to help us find an altitude x, leg b, and leg a of a right triangle. We estimate the height of a statue using the corollaries.

Algebra I #3.9c, Proportions - Means and Extremes

https://www.youtube.com/watch?v=AsNYLh9CF_0&index=91&list=PLKi4WTp6PRGXzkjUUMYVChM2WxWfgIrK4

Geometry 7.3b, Proofs with Similar Triangles

https://youtu.be/ZoKmUu-o4Po

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Bitsy and Lola don't wrestle often because Bitsy has trouble breathing most of the time. I caught a rare play fight between them that ended with Lola pawing the air while on her back (she does this often).

An explanation of Direct Variation as a linear relationship between two variables, x and y, that can be written in the form y = xk, where the k is a nonzero constant. In algebra if y varies directly as x, then y = kx or y/x = k, where k is the constant of variation. We find if the relationship between the scale factor and the perimeter of a figure is a direct variation. We make a table to record data for our scale factor x, length, width, and perimeter. We graph the ordered pairs to see if the points are collinear and include the origin (0,0). We find the equation of direct variation and find the constant of variation.

Geometry 7.6a, Dilations & Similarity in the Coordinate plane

https://youtu.be/kCUuiyP7Jdc

Geometry 7.6b, Segment Partition

https://youtu.be/uejqZuqS4Ec

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A directed line segment is a segment between two points with a specified direction. To partition a directed line segment is to divide it into two segments with a given ratio. We find the coordinates of a point in a directed line segment that has a ratio of 3/4, which is a 75% partition point. We use a compass and straightedge to construct a point in a directed line segment with a ratio of 1 to 2 for the partition point.

Geometry 7.6a, Dilations & Similarity in the Coordinate plane

https://youtu.be/kCUuiyP7Jdc

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how a dilation is like a JPEG image being enlarged or reduced using coordinates and similarity to change the images size. A recap of the meaning of a dilation, scale factor, and the scale factor k. We have a computer graphics application example with a dilation of scale factor 5/2, in which we find the ordered pairs of the enlarged image. We find coordinates of similar triangles using a scale factor. We prove that two triangles are similar using given points and the Distance Formula along with the Reflexive Property and Side-Angle- Side Similarity Theorem. We use the Distance Formula and SSS Similarity Theorem to find a similarity ratio between two triangles. (At 7:05, I accidentally used an approximation symbol instead of the needed congruent symbol. Sorry!)

https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of similarity ratio, perimeter ratio, and area ratio. We discuss the Proportional Perimeters and Areas Theorem that tells us the similarity ratio of corresponding sides is equal to the perimeter ratio. It also tells us the area ratio is equal to the square of the similarity ratio, and it is equal to the square of the perimeter ratio. We use ratios, and our new theorem, to find the perimeter and area of a similar triangle, we also use it to find the perimeter and area of a similar rectangle.

Geometry 7.5a, Indirect Measurement & Scale Drawing

https://youtu.be/b-WbJQRb2pY

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An explanation of the Triangle Angle Bisector Theorem and how we can use it to find segment lengths of a triangle. How an angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the length of the other two sides.

Geometry 7.4a, Triangle Proportionality Theorem & its Converse

https://youtu.be/WASfbl75RxU

Geometry 7.4b, Two-Transversal Proportionality Corollary

https://youtu.be/TySYchu5Nf4

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An explanation of the Triangle Proportionality Theorem and its importance in making perspective drawings. We find the missing length of a segment of a triangle using the Triangle Proportionality Theorem. We verify that a segment is parallel to another segment of a triangle using the Converse of the Triangle Proportionality Theorem. We then construct a line parallel to the base of a triangle, using a compass and straightedge, that is proved by the Converse of the Triangle Proportionality Theorem.

Linear Perspective in Art & Fillipo Brunelleschi

https://www.britannica.com/art/linear-perspective

Beginner Drawing: Linear Perspective: The Basics

https://www.artistsnetwork.com/art-techniques/beginner-artist/beginner-drawing-linear-perspective-the-basics/

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An explanation of how we can prove the Pythagorean theorem by using similar triangles. We draw an altitude inside the right triangle to create two new triangles that are similar to the original. We then write proportions to prove the Pythagorean theorem. We also do a regular ladder problem that involves the Pythagorean theorem.

Geometry 7.3a, AA, SSS, SAS Triangle Similarity

https://youtu.be/8HX751kZyzo

Geometry 7.3b, Proofs with Similar Triangles

https://youtu.be/ZoKmUu-o4Po

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Education for everyone!

I have over 2,600 Math videos on YouTube, ranging from 1st grade through Algebra 2.

It would be impossible for me to upload all of them onto BitChute.

I've included most of my GED Math videos, and the Grade 1 videos will auto upload from now on.

I planning to do Geometry, Trigonometry, then Pre-Calculus Playlist in the future.

You can study an entire grade level of Math, lesson by lesson with my playlists, in order.

Catch up to your class, work ahead, pass the GED, or place higher on college entry tests to avoid remedial classes.

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