# JoAnn's School

An explanation of our first theorem which says an inscribed angle subtends a semicircle if and only if the angle is a right angle, a review of the meaning of subtend, we find angle measures in inscribed triangles. An explanation of the second theorem which says if a quadrilateral is inscribed in a circle, then it's opposite angles are supplementary. We find angle measures of an inscribed quadrilateral, we find the value of y in an algebraic angle measure. We discuss how we know if a segment is a diameter of a circle or not by whether it goes through the center point.

Geometry 12.4a, Inscribed angle, Intercepted arc, Subtends

https://youtu.be/HR96bkdM2Dg

High School Geometry Playlist

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

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We start the lesson with the review of probability, event, result of a probability experiment, outcome, and sample space. Probabilities are written as fractions or decimals from 0 to 1, or as percentages from 0% to 100%. Equally likely outcomes have the same chance of occurring. Favorable outcomes are outcomes in a specified event. Theoretical probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. We find the probability of an event that a spinner will point to a particular color, then we find the probability that a nickel, dime, and quarter will land the same way when they are flipped. We discuss the complement of an event with an example. We find the probability of an event by using a permutation.

I just picked her up an hour ago and this short video was taken at the vet's office. She's very groggy, but she's okay! What a resilient little girl! The vet's staff was wonderful and caring. They sent me a text message right after the surgery to let me know that she was hanging in there. She's about 15 years old now, and hopefully I have a few more years with her.

She will need to wear a plastic collar for 10 days to make sure she doesn't lick her incision. She has antibiotics and pain relievers to take. After 10 days we need to return to the vet to have the stitches removed and her wound checked.

Right now she is somewhat comfortable, on a big dog bed that is covered with plastic, towels, and a sheet.

The incision is kind of zig-zag shaped and long. It's very close to her right rear leg, so she has trouble walking. The mass was about 4 inches in diameter! It was BIG! They are sending it to a lab to have it analyzed. Thank you to everyone for your concern!

She made it home okay! XXXOOO

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An explanation of an inscribed angle as an angle whose vertex is on a circle and whose side's contain chords, an intercepted arc as an arc with endpoints that lie on the sides of an inscribed angle and all the points of the circle between them, a chord or arc subtends an angle if its endpoints lie on the sides of the angle. We discuss the Inscribed Angle theorem, and write a paragraph proof to prove that an angle is half the measure of its intercepted arc. We find measures of arcs and inscribed angles using the Inscribed Angle theorem. We explain Corollary 12.4.2 which says if inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc, then the angles are congruent. We find the measure of an angle that is inscribed in a circle from string art.

String Art

https://www.youtube.com/watch?v=y-5VmBZbbZ8

Geometry 5.2b, Incenter Theorem & Inscribed circles

https://youtu.be/Kb0RJ3IvOvM

High School Geometry Playlist

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

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Surgery moved up to tomorrow, Feb 15, 2019. The mass is growing too quickly, the vet and I are afraid that it's going to affect her health. So, we can't wait until the 28th when the surgery was previously scheduled. It might affect her walking because it's growing so fast. I don't know what the outcome is going to be. I'm either going to be taking care of Bitsy recovering from surgery, or I'm going to be grieving the loss of Bitsy. If you don't see my normal math posts to the channel don't be too alarmed. We'll see how it goes! Please consider donating to her medical costs through PayPal, YouTube fanfunding , or Patreon.

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An explanation of the difference between degrees and radians, the relationship between the radius and arc length of a central angle as a Radian, the Greek letter Theta as a symbol to represent the name of an angle, using the superscript for degrees with Theta to represent the measure of angle Theta in degrees, using the superscript capital R to represent the measure of angle Theta in radians. We discuss several examples of converting angle measures from degrees to radians, then radians to degrees. We use theta notation in a proportion to convert degrees to radians, then radians to degrees (which is taught in trigonometry and pre-calculus).

Theta information https://en.wikipedia.org/wiki/Theta

Geometry 12.3a, Sector of a circle & Sector area

https://youtu.be/SkVnNGsOA8o

Geometry 12.3b, Area of a Segment of a circle

https://youtu.be/Tdxns7t0O1o

Geometry 12.3c, Arc length of a Circle

https://youtu.be/fdJnThLjyPg

High School Geometry Playlist

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

TWITTER https://twitter.com/JoannsSchool

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An explanation of an arc of length, how to use a formula or a proportion to find an arc length. We solve our examples in terms of Pi, then rounded to the nearest hundredth.

Geometry 12.2a, Major Arc, Minor Arc, Arc Addition Postulate

https://youtu.be/EOPnL4_YWxc

Geometry 12.2b, Congruent angles, arc, chords, & 3 Theorems

https://youtu.be/O9KzimmPl9o

Geometry 12.3a, Sector of a circle & Sector area

https://youtu.be/SkVnNGsOA8o

Geometry 12.3b, Area of a Segment of a circle

https://youtu.be/Tdxns7t0O1o

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

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As many of you know, I took Bitsy to the vet yesterday Monday February 11th, 2019. I had found a large mass a few days ago. This is an update after we went to the vet, she had X-rays of her chest and abdominal area. Please consider donating to her vet bills. I need $1,300. See links below.

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An explanation of a segment of a circle as a region bounded by an arc and its chord, how the area of a segment is equal to the area of a sector minus the area of a triangle within that sector. We have two examples of finding the area of a segment of a circle and rounding it to the nearest hundredth.

Geometry 5.8b, 30°-60°-90° Triangle Theorem

https://youtu.be/KLWEVm6SaEQ

Geometry 12.3a, Sector of a circle & Sector area

https://youtu.be/SkVnNGsOA8o

Geometry 10.3b, Triangle Area Formulas unknown height, Heron's Formula

https://youtu.be/N8gwjgfO2fE

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An explanation and definition of a sector of a circle, and the formula we would use to find the area of a sector. We find the area that is watered by a Center Pivot irrigation system sprinkler that rotates through an angle of 50 degrees on a circular plot.

Center pivot irrigation system

https://en.wikipedia.org/wiki/Center_pivot_irrigation

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I'm angry with myself for not noticing this before! I was trimming Bitsy's paws this morning and found a huge golf ball-sized lump between her legs. She's had such a rough life, she's been through so much. I adopted her in 2013, and she was very sick. I raised the money to treat her heartworm, pancreatitis, intestinal worms, cover her dental work, and she's had six wonderful years living with me with love. They estimated her age to be around 9 or 10 years old when I found her so she's around 15 or 16 years old now. We believe she's a Pomeranian mix and considering how rough her life was before she probably doesn't have the life expectancy of a regular Pomeranian. Keep her in your thoughts. I'll keep everyone updated with the vet visit and what they think it is.

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An explanation of congruent arcs as two arcs that have the same measure, Theorem 12.2.2 which says congruent central angles have congruent chords, congruent chords have congruent arcs, and congruent arcs have congruent central angles. The converses of the parts of this theorem are also true. We do a two-column proof to show that two chords are congruent, we find the measure of an arc by using algebra, we find a central angle measure for one of two congruent circles. Theorem 12.2.3 says in a circle, if a radius (or diameter) is perpendicular to a chord, then it bisects the chord and its arc. Theorem 12.2.4 says in a circle, the perpendicular bisector of a chord is a radius (or diameter). We find the length of a chord using radii and the Pythagorean theorem.

Geometry 12.2a, Major Arc, Minor Arc, Arc Addition Postulate

https://youtu.be/EOPnL4_YWxc

Geometry 4.5b, Side-Angle-Side (SAS) congruence & construct triangles using SAS

https://youtu.be/ZY0T1V1Ja_I

Geometry 4.7a, CPCTC Triangle Congruence & the Distance Formula

https://youtu.be/vuC40Hg4OHU

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

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The definition and explanation of minor arcs, major arcs, and their measures. We discuss that if the endpoints of an arc lie on a diameter, the arc is a semicircle, which is equal to 180°. We find the measure of an arc from a circle graph, discuss adjacent arcs as arcs of the same Circle that intersect at exactly one point, and understand the Arc Addition Postulate. We use the Arc Addition Postulate to find the measure of an arc. We find the length of an arc by using a formula and the measure of central angle, then we see how we can find the length of an arc by using a proportion.

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

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An explanation of circle graphs and how they compare data that are parts of a whole unit. A central angle is an angle whose vertex is the center of the circle. We make a circle graph to represent data given in a table, we color each section of the circle to match the data.

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

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A step-by-step explanation of how to use a compass and straightedge to construct a tangent line to a circle at a point.

Geometry 3.4c, Construct Perpendicular line to a given line through a given point https://www.youtube.com/watch?v=DlFrzkMGfUc&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3&index=31

Draw with compass & straightedge playlist

https://www.youtube.com/playlist?list=PLKi4WTp6PRGUeo2NEs6yiLManPgRzez0e

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

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An explanation of congruent circles as two circles that have congruent radii, concentric circles as co-planar with the same center point, tangent circles as two co-planar circles that intersect at exactly one point. Tangent circles can be internally tangent or externally tangent. We find the length of each radius of internally tangent circles, identify the point of tangency, then write the equation of the tangent line at this point. We discuss common external tangents and common internal tangents. We use our theorems to help us solve some example problems such as finding the distance from the summit of Mount Everest to the horizon to the nearest mile, and finding the length of segments drawn tangent to a circle from an exterior point.

Geometry 12.1a, Introducing Chord, Secant, Tangent, lines that intersect circles

https://youtu.be/AEU61AWsx8k

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An explanation of the notation used to label a circle, interior and the exterior of a circle, an introduction to lines and segments that intersect circles as a chord, secant, or tangent (and the point of tangency). We discuss how a secant can contain a chord, how a chord can be a diameter or two radii.

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An explanation of the formula for the surface area of a sphere, how the surface area of a sphere is four times the area of its Great Circle, finding the surface area of a sphere with a given diameter and putting our answer in terms of Pi, finding the volume of a sphere with a given surface area, exploring the effects of changing the dimensions of volume if the radius of a sphere is tripled. Finally, we find the surface area and volume of a composite figure which is made of a cone and hemisphere.

Geometry 11.4a, Volume of a Sphere or Hemisphere

https://youtu.be/dW3qrnlCv1Q

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

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An explanation of a sphere as the locus of points in space that are a fixed distance from a given point called the "center of a sphere". A "radius of a sphere" connects the center of a sphere to any point on the sphere. A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres. We use the volume of a sphere formula to find the volume of a sphere and put our answer in terms of Pi. We then use the volume of a hemisphere formula to find the volume of a hemisphere and put our answer in terms of Pi. We compare the volumes of two different balls to see how many times greater one is than the other. Finally, we prove that the shaded cross-sections of a hemisphere and a cylinder with a cone removed from its interior have equal area if both have radius and height equal to r.

Geometry 11.2a, Volume of Prisms & Cavalieri's Principle

https://youtu.be/D16LYhRZgE8

Geometry 11.2b, Volume of Cylinders & Cavalieri's Principle

https://youtu.be/jV803JQ2W2Q

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

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An explanation of cube roots, an index, and the radicand of a radical. We find the side length of a cube with a given volume. We discuss what happens to the root if the index of the radical is even.

Algebra I #11.3c,

What are Cube Roots

https://youtu.be/R0urqn1nR8w

Algebra II 7.1A, Square Roots, Principal Square Roots & 2 Theorems

https://www.youtube.com/watch?v=5vMF4o2_bFQ&index=141&list=PLKi4WTp6PRGVGCVa4jrZLB7zFNG3mRg0N

Algebra II 7.1B, Odd and Even Roots (indexes)

https://www.youtube.com/watch?v=Ez7tsDFGaXk&list=PLKi4WTp6PRGVGCVa4jrZLB7zFNG3mRg0N&index=142

Algebra II 7.1C, Kth Roots & Odd and Even Roots

https://www.youtube.com/watch?v=2euX9JrAt70&index=143&list=PLKi4WTp6PRGVGCVa4jrZLB7zFNG3mRg0N

Geometry 11.3a, Volume of Pyramids

https://youtu.be/JSoVdP1uHyA

Geometry 11.3b, Volume of Cones

https://youtu.be/9rzM3bCbocg

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

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An explanation of how to find the volume of cones using the volume of cone formula. We find the volume of a cone with a given radius and height, we find the volume of a cone with a given base circumference and a height that is 3 cm less than twice the radius, we use the Pythagorean theorem to find a height, we then explore the effects of changing dimensions and what happens when the length, width, and height of a rectangular pyramid are multiplied by 1/4. For last example we find the volume of a 3D composite figure that contains a cone and cylinder, then we see what happens to the volume of that composed figure if the cone is inverted into the cylinder.

Geometry 11.2a, Volume of Prisms & Cavalieri's Principle

https://youtu.be/D16LYhRZgE8

Geometry 11.2b, Volume of Cylinders & Cavalieri's Principle

https://youtu.be/jV803JQ2W2Q

Off grid rainwater harvesting in Hawaii.

https://www.youtube.com/watch?v=CC41EDNWtbg&t=3s

Geometry 11.2c, Finding Volumes of Composite 3D figures

https://youtu.be/JT9i6bfin8w

Geometry 11.3a, Volume of Pyramids

https://youtu.be/JSoVdP1uHyA

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

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An explanation of how the volume of a pyramid is related to the volume of a prism with the same base and height. We divide a cube into three congruent Square pyramids using Nets. We use the formula for the volume of a pyramid to find the volume of a rectangular pyramid, then a square pyramid, trapezoidal pyramid, and finally a regular hexagonal pyramid whose height is the same as its apothem.

Geometry 5.8b, 30°-60°-90° Triangle Theorem

https://youtu.be/KLWEVm6SaEQ

Geometry 10.1c, Area of Triangles & Trapezoids

https://youtu.be/M7KOvEOd-mg

Geometry 10.2c, Area of Regular Polygons with the Apothem

https://youtu.be/_yetNuzt8SY

Moody Gardens info:

https://en.wikipedia.org/wiki/Moody_Gardens

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A quick review of the formulas we learned in lesson 11.2a and 11.2b, then an explanation of how we can find the volume of a composite three-dimensional figure by finding the volume of each separate figure, then finding the sum or difference of their volumes.

Geometry 11.2a, Volume of Prisms & Cavalieri's Principle

https://youtu.be/D16LYhRZgE8

Geometry 11.2b, Volume of Cylinders & Cavalieri's Principle

https://youtu.be/jV803JQ2W2Q

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An explanation of the volume of a three-dimensional figure, such as a cylinder, as the number of non-overlapping unit cubes of a given size that will exactly fill the interior. I explain Cavalieri's Principle which says if two 3D figures have the same height and same cross-sectional area at every level, they have the same volume. We discuss the formula for the volume of a cylinder as V=Bh or V= πr²h. We find the volume of a cylinder and give our answer in terms of Pi or as rounded to the nearest tenth. We find the volume of a steel rainwater tank, then the volume of a cylinder with a base area of 36π inches squared, and finally we find the effects of changing dimensions of a cylinder by multiplying the radius and height by half.

Geometry 11.2a, Volume of Prisms & Cavalieri's Principle

https://youtu.be/D16LYhRZgE8

Off grid rainwater harvesting in Hawaii.

https://www.youtube.com/watch?v=CC41EDNWtbg&t=3s

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An explanation of the volume of prisms as the number of non-overlapping unit cubes of a given size that will exactly fill the interior of a figure. Cavalieri's Principle says if two 3D figures have the same height and the same cross-sectional area at every level, they have the same volume. We learn how to find the volume of a prism whether it is a right prism or an oblique prism. We find the volume of a right regular pentagonal prism with given base edge and length by finding the apothem and using a tangent ratio to help us find the base area. We find how much an aquarium holds in gallons and the weight of those gallons in pounds.

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

https://youtu.be/z_r8PGb-NqM

Geometry 10.2c, Area of Regular Polygons with the Apothem

https://youtu.be/_yetNuzt8SY

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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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