JoAnn's School

JoAnnsSchool

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

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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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

High School Geometry Playlist
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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

High School Geometry Playlist
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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!)

High School Geometry Playlist
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

High School Geometry Playlist
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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

High School Geometry Playlist
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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/

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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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

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how all circles are similar because they have the same shape. We can prove this by using a dilation whose center of dilation is not (0, 0) the origin. We prove two circles are similar by using a center (0,0) for Circle A and a center (5,0) for Circle B with a radius of 2. Then we have another example where we prove that Circle C with a center (-2, 0) and radius 2 is similar to Circle D with Center (4,1) and radius 3. We figure out how quilt pattern blocks can be drawn with a scale factor of 3 using a coordinate plane. We use transformations to determine whether two polygons are similar by determining whether one figure can be mapped to the other by a similarity transformation.

Geometry 7.2a, Dilations & Similarity Transformations
https://youtu.be/ppdt9z0HxSU

High School Geometry Playlist
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An explanation of a dilation as a transformation that maps (x,y) to (kx, ky) where k is greater than 0, has a center at (0,0), and scale factor k. How similarity ratios are scale factors, drawing and describing dilations, how the pre-image and image of dilations are similar, similarity transformations, and finally determining whether polygons are similar.

High School Geometry Playlist
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An explanation of how figures that are similar will have the same shape but not the same size. We learn the geometric notation for similar as a tilde ~, and the properties of similar polygons. We discuss the similarity ratio as a ratio of the lengths of the corresponding sides of two similar polygons. We identify the pairs of congruent angles and corresponding sides of a polygon and find their similarity ratio. We determine whether polygons are similar by comparing the corresponding angles and sides.

High School Geometry Playlist
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An explanation of how to construct a kite figure using a compass and a straightedge.

Drawing with a compass and straightedge playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGUeo2NEs6yiLManPgRzez0e

High School Geometry Playlist
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An explanation of a trapezoid as a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base, and the nonparallel sides are called the legs. Base angles of a trapezoid are two consecutive angles whose common side is a base. If the legs of a trapezoid are congruent, the trapezoid is an isosceles trapezoid. We have three theorems for the Properties of Isosceles Trapezoids, we find an angle measure, and then a side length, using the properties of Isosceles trapezoids, we find the value of a variable so that a trapezoid "is" isosceles. We discuss the mid-segment of a trapezoid as the segment whose endpoints are the midpoints of the legs. We discuss the Trapezoid Mid-segment theorem and use it to find the length of a base. We compare the Trapezoid Mid-segment theorem to the Triangle Mid-segment theorem to see the difference between their formulas.

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 6.6b, Isosceles Trapezoids & Midsegment of Trapezoids & 4 Theorems
https://youtu.be/ryLKnGvhgDs

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An explanation of a kite as a quadrilateral with exactly two pairs of congruent consecutive sides and its diagonals are not congruent. We have two theorems for the properties of kites, we work a proof for the second theorem which says if a quadrilateral is a kite then exactly one pair of opposite angles are congruent. We find the perimeter of a kite by using the Pythagorean theorem and properties of kites to find the side lengths. We find unknown angle measures using the properties of kites.

High School Geometry Playlist
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(Sorry, ERROR AT 4:21, should be BD and not BC, we're finding the diagonals) An explanation of how we can prove that a given quadrilateral is a rectangle, rhombus, or square by using the definitions of the special quadrilaterals. We apply the conditions for special parallelograms to determine if a conclusion is valid, we identify special parallelograms in the coordinate plane using diagonals to determine whether a parallelogram with given vertices is a rectangle, rhombus, or square. We use the Distance Formula and the Slope Formula to help us do this.

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 6.5a, Conditions for Rectangles & Rhombuses, 5 Theorems
https://youtu.be/XU1YGUfMzDY

Algebra I Radical Expressions & Equations Playlist, Chapter 11
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVwqn3G4ZWKhR4BG8wAjccg

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An explanation of the conditions for rectangles with two theorems, the conditions for rhombuses with three theorems, and a two-column proof to prove that a parallelogram is a rhombus using our fifth theorem from this video.

High School Geometry Playlist
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A step-by-step description of how to construct a rhombus with a compass and a straightedge.

Geometry 1.3, Measuring & constructing angles
https://www.youtube.com/watch?v=6fO-xhWSYzo&index=4&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 3.3c, Rhombus Method to construct parallel lines
https://www.youtube.com/watch?v=DZJAxcMVALY&index=28&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 3.4a, Construct a Perpendicular bisector of a segment
https://www.youtube.com/watch?v=irq3kSSS8kA&index=29&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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

Geometry 4.5b, Side-Angle-Side (SAS) congruence & construct triangles using SAS
https://www.youtube.com/watch?v=ZY0T1V1Ja_I&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3&index=46

Geometry 4.6a, Angle-Side-Angle (ASA) Congruence & construct triangles using ASA
https://www.youtube.com/watch?v=icYWnmmx4s0&index=47&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 5.2a, Circumcenter of a Triangle & Circumcenter Theorem
https://www.youtube.com/watch?v=BRlgvjLZwVw&index=59&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 5.3a, Centroid Theorem & construct Centroid of a Triangle
https://www.youtube.com/watch?v=Crax3yFg-y0&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3&index=61

Geometry 5.3b, Altitude of a Triangle & finding the Orthocenter
https://www.youtube.com/watch?v=lFmpNVHjAAs&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3&index=62

Geometry 5.4b, Construct the Midsegment of a triangle with a compass
https://www.youtube.com/watch?v=j8Y9crWqBcg&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3&index=64

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how a square is a quadrilateral with four right angles and four congruent sides, and how a square is a parallelogram, a rectangle, AND a rhombus. We verify the properties of a square by showing that the diagonals of the square are congruent perpendicular bisectors of each other by using the Distance Formula, then using the Slope Formula, and finally by using the Midpoint Formula. We use the properties of special parallelograms in a two-column proof to show that a triangle within a rectangle is isosceles. We review the properties of special parallelograms and compare them to each other.

Geometry 6.4a, Properties of Rectangles & 2 Theorems
https://www.youtube.com/watch?v=-kNkdJhYrG4&index=84&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

Geometry 6.4b, Properties of Rhombuses & 3 Theorems
https://www.youtube.com/watch?v=yz3BC6k0vmM&index=85&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

High School Geometry Playlist
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An explanation of the properties of rhombuses (or rhombi) and how a rhombus is also a special quadrilateral. We discuss the three properties of rhombuses as theorems, we do a paragraph proof with the third theorem which says, "If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles". We find the side length of a rhombus by using the definition of a rhombus and substituting values for x, we find a missing angle measure by using the theorem that says, "If a parallelogram is a rhombus, then it's diagonals are perpendicular".
Geometry 6.4a, Properties of Rectangles & 2 Theorems
https://www.youtube.com/watch?v=-kNkdJhYrG4&index=84&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

High School Geometry Playlist
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An explanation of how a rectangle is a special type of quadrilateral with four right angles, the properties of rectangles in two theorems, how a rectangle is a parallelogram that inherits all the properties of parallelograms, we find a segment that is half of a diagonal, and we find a segment that is the length of a diagonal.

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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We do a review of the definition of a parallelogram and the five properties of a parallelogram that we learned in the previous video 6.3a. We show that a quadrilateral is a parallelogram using 4 given ordered pairs and the definition of a parallelogram, we show that a quadrilateral is a parallelogram using 4 ordered pairs and Theorem 6.3.1, we look at a parallelogram mount for binoculars to see why it will always be a parallelogram.

Geometry 6.3a, Conditions for Parallelograms & 5 Theorems
https://youtu.be/IsF3IWw82Zg

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of the five theorems for the conditions of parallelograms and how we'll be working with the converse situation to our two previous videos 6.2a and 6.2b. We'll do a paragraph proof for theorem 6.3.1, we determine if a quadrilateral is a parallelogram by applying the conditions necessary, we verify that figures are parallelograms which have sides that are algebraic expressions with given values for x and y.

Geometry 6.2a, Properties of Parallelograms 4 Theorems
https://www.youtube.com/watch?v=CKy195xphLQ&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3&index=81

Geometry 6.2b, Parallelograms in the Coordinate Plane & prove Opposite Angles Congruent
https://www.youtube.com/watch?v=d7w02x2k7Ac&index=82&list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of how to find a fourth point for a vertex of a parallelogram on a coordinate plane by using the slope formula, and using Properties of Parallelograms in a proof to prove angles are congruent.

Geometry 6.2a, Properties of Parallelograms 4 Theorems
https://youtu.be/CKy195xphLQ

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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An explanation of the special properties of quadrilaterals, 4 theorems about those properties, a two-column proof for the first property that the opposite sides of a parallelogram are congruent, how two parallel lines cut by two transversals will make a parallelogram, for the remaining three theorems for parallelograms we discuss how the opposite angles are congruent, consecutive angles are supplementary, and how the diagonals will bisect each other. We find missing angle measures using the theorems and algebra.

High School Geometry Playlist
https://www.youtube.com/playlist?list=PLKi4WTp6PRGVBM1nPhwW1lTuxi32Q0IZ3

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Created 8 months, 3 weeks ago.

389 videos

CategoryEducation

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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YOUTUBE FAN FUNDING on my channel Home page
https://www.youtube.com/channel/UCAZKtYcE5Jgd6hVL-RHv6Vw

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