 ## What's New And Recent Updates:

### Ptolemy’s Theorem (examples, solutions, videos, worksheets, homework, lesson plans)

Ptolemy’s Theorem, determine the area of a cyclic quadrilateral as a function of its side lengths and the acute angle formed by its diagonals, prove Ptolemy’s theorem, examples and step by step solutions, Common Core Geometry

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### Cyclic Quadrilaterals (examples, solutions, videos, worksheets, homework, lesson plans)

Cyclic Quadrilaterals, a quadrilateral is cyclic if and only if its opposite angles are supplementary, derive and apply the area of cyclic quadrilateral ABCD as 1/2 AB·CD·sin(w), examples and step by step solutions, Common Core Geometry

### Equations for Tangent Lines to Circles (examples, solutions, videos, worksheets, homework, lesson plans)

Equations for Tangent Lines to Circles, Given a circle, students find the equations of two lines tangent to the circle with specified slopes, find the equation of the line tangent to the circle from that point, examples and step by step solutions, Common Core Geometry

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### Recognizing Equations of Circles (examples, solutions, videos, worksheets, homework, lesson plans)

Recognizing Equations of Circles, complete the square in order to write the equation of a circle in center-radius form, recognize when a quadratic in x and y is the equation for a circle, examples and step by step solutions, Common Core Geometry

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### Writing the Equation for a Circle (examples, solutions, videos, worksheets, homework, lesson plans)

Writing the Equation for a Circle, write the equation for a circle in center-radius form using the Pythagorean theorem or the distance formula, examples and step by step solutions, Common Core Geometry

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### CIE May 2021 9709 Prob & Stats 1 Paper 52

CIE May 2021 9709 Prob & Stats 1 Paper 52, Past Papers, 9709/52, Mark Scheme, step by step solutions

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### Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams (examples, solutions, videos, worksheets, homework, lesson plans)

Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams, find missing lengths in circle-secant or circle-secant-tangent diagrams, examples and step by step solutions, Common Core Geometry

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### Secant Angle Theorem, Exterior Case (examples, solutions, videos, worksheets, homework, lesson plans)

Secant Angle Theorem, Exterior Case, find the measures of angle/arcs and chords in figures that include two secant lines meeting outside a circle, examples and step by step solutions, Common Core Geometry

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### Secant Lines; Secant Lines That Meet Inside a Circle (examples, solutions, videos, worksheets, homework, lesson plans)

Secant Lines; Secant Lines That Meet Inside a Circle, an angle whose vertex lies in the interior of a circle intersects the circle in two points and that the edges of the angles are contained within two secant lines of the circle, angle whose vertex lies in the interior of a circle is equal to half the sum of the angle measures of the arcs intercepted by it and its vertical angle, examples and step by step solutions, Common Core Geometry

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### The Inscribed Angle Alternate—A Tangent Angle (examples, solutions, videos, worksheets, homework, lesson plans)

The Inscribed Angle Alternate—A Tangent Angle, use the inscribed angle theorem to prove other theorems in its family, solve missing angle problems using the inscribed angle theorem, solve a variety of missing angle problems using the inscribed angle theorem, examples and step by step solutions, Common Core Geometry

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### Tangent Segments (examples, solutions, videos, worksheets, homework, lesson plans)

Tangent Segments, use tangent segments and radii of circles to conjecture and prove geometric statements, use the fact if a circle is tangent to both rays of an angle, then its center lies on the angle bisector, examples and step by step solutions, Common Core Geometry

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### Properties of Tangents (examples, solutions, videos, worksheets, homework, lesson plans)

Properties of Tangents, a line is tangent to a circle at a given point if it is perpendicular to the radius drawn to that point, construct tangents to a circle through a given point, examples and step by step solutions, Common Core Geometry

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### Unknown Length and Area Problems (examples, solutions, videos, worksheets, homework, lesson plans)

Unknown Length and Area Problems, apply their understanding of arc length and area of sectors to solve problems of unknown area and length, examples and step by step solutions, Common Core Geometry

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### Arc Length and Areas of Sectors (examples, solutions, videos, worksheets, homework, lesson plans)

Arc Length and Areas of Sectors, how to determine the length of an arc and the area of a sector, examples and step by step solutions, Common Core Geometry

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### Arcs and Chords (examples, solutions, videos, worksheets, homework, lesson plans)

Arcs and Chords, Congruent chords have congruent arcs, Arcs between parallel chords are congruent, examples and step by step solutions, Common Core Geometry

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### The Angle Measure of an Arc (examples, solutions, videos, worksheets, homework, lesson plans)

The Angle Measure of an Arc, Define the angle measure of arcs, and understand that arcs of equal angle measure are similar, The measure of an inscribed angle is half the angle measure of its intercepted arc, Explain and understand that all circles are similar, examples and step by step solutions, Common Core Geometry

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### Unknown Angle Problems with Inscribed Angles in Circles (examples, solutions, videos, worksheets, homework, lesson plans)

Unknown Angle Problems with Inscribed Angles in Circles, Use the inscribed angle theorem to find the measures of unknown angles, examples and step by step solutions, Common Core Geometry

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### Inscribed Angle Theorem and Its Applications (examples, solutions, videos, worksheets, homework, lesson plans)

Inscribed Angle Theorem and Its Applications, Recognize and use different cases of the inscribed angle theorem embedded in diagrams, examples and step by step solutions, Common Core Geometry

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### Experiments with Inscribed Angles (examples, solutions, videos, worksheets, homework, lesson plans)

Experiments with Inscribed Angles, relationship between inscribed angles and central angles and their intercepted arcs, examples and step by step solutions, Common Core Geometry

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### Rectangles Inscribed in Circles (examples, solutions, videos, worksheets, homework, lesson plans)

Rectangles Inscribed in Circles, symmetries of inscribed rectangles across a diameter, examples and step by step solutions, Common Core Geometry

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### Circles, Chords, Diameters, and Their Relationships (examples, solutions, videos, worksheets, homework, lesson plans)

Circles, Chords, Diameters, and Their Relationships, Identify the relationships between the diameters of a circle and other chords of the circle, examples and step by step solutions, Common Core Geometry

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### Thales’ Theorem (examples, solutions, videos, worksheets, homework, lesson plans)

Thales’ Theorem, explore the converse of Thales' theorem, Prove the statement of Thales' theorem, examples and step by step solutions, Common Core Geometry

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### The Distance from a Point to a Line (examples, solutions, videos, worksheets, homework, lesson plans)

The Distance from a Point to a Line, name several points on a line given by a parametric equation and provide the point-slope equation for a line given by a parametric equation, determine whether lines given parametrically are parallel or perpendicular, examples and step by step solutions, Common Core Geometry

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### Motion Along a Line—Search Robots Again (examples, solutions, videos, worksheets, homework, lesson plans)

Motion Along a Line—Search Robots Again, name several points on a line given by a parametric equation and provide the point-slope equation for a line given by a parametric equation, determine whether lines given parametrically are parallel or perpendicular, examples and step by step solutions, Common Core Geometry

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### 2021 Physics 9702 Paper 22

2021 Physics 9702 Paper 22, Past Papers, 9702/22, Mark Scheme, step by step solutions

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### 2020 Physics 9702 Paper 23

October 2020 Physics 9702 Paper 23, Past Papers, 9702/23, Mark Scheme, step by step solutions

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### Analytic Proofs of Theorems Previously Proved by Synthetic Means (examples, solutions, videos, worksheets, homework, lesson plans)

Analytic Proofs of Theorems Previously Proved by Synthetic Means, prove that the intersection of the medians of a triangle meet at a point that is two-thirds of the way along each median from the intersected vertex, prove the diagonals of a parallelogram bisect one another and meet at the intersection of the segments joining the midpoints of opposite sides, examples and step by step solutions, Common Core Geometry

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### CIE May 2021 9709 Prob & Stats 2 Paper 63

CIE May 2021 9709 Prob & Stats 2 Paper 63, Past Papers, 9709/63, Mark Scheme, step by step solutions

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### Dividing Segments Proportionately (examples, solutions, videos, worksheets, homework, lesson plans)

Dividing Segments Proportionately, find midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts, examples and step by step solutions, Common Core Geometry

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### Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities (examples, solutions, videos, worksheets, homework, lesson plans)

Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities, find the perimeter of a triangle or quadrilateral in the coordinate plane given a description by inequalities, find the area of a triangle or quadrilateral in the coordinate plane given a description by inequalities by employing Green’s theorem, examples and step by step solutions, Common Core Geometry

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### Perimeter and Area of Polygonal Regions in the Cartesian Plane (examples, solutions, videos, worksheets, homework, lesson plans)

Perimeter and Area of Polygonal Regions in the Cartesian Plane, find the perimeter of a quadrilateral in the coordinate plane given its vertices and edges, find the area of a quadrilateral in the coordinate plane given its vertices and edges by employing Green’s theorem, examples and step by step solutions, Common Core Geometry

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### Perimeter and Area of Triangles in the Cartesian Plane (examples, solutions, videos, worksheets, homework, lesson plans)

Perimeter and Area of Triangles in the Cartesian Plane, find the perimeter of a triangle in the coordinate plane using the distance formula, state and apply the formula for area of a triangle with vertices, examples and step by step solutions, Common Core Geometry

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### Parallel and Perpendicular Lines (examples, solutions, videos, worksheets, homework, lesson plans)

Parallel and Perpendicular Lines, recognize parallel and perpendicular lines from slope, examples and step by step solutions, Common Core Geometry

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### Equations for Lines Using Normal Segments (examples, solutions, videos, worksheets, homework, lesson plans)

Equations for Lines Using Normal Segments, apply the criterion to determine if two segments are perpendicular, examples and step by step solutions, Common Core Geometry

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### Segments That Meet at Right Angles (examples, solutions, videos, worksheets, homework, lesson plans)

Segments That Meet at Right Angles, apply the criterion to determine if two segments are perpendicular, examples and step by step solutions, Common Core Geometry

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### Criterion for Perpendicularity (examples, solutions, videos, worksheets, homework, lesson plans)

Criterion for Perpendicularity, explain the connection between the Pythagorean Theorem and the criterion for perpendicularity, examples and step by step solutions, Common Core Geometry

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### Designing a Search Robot to Find a Beacon (examples, solutions, videos, worksheets, homework, lesson plans)

Designing a Search Robot to Find a Beacon, find the segments obtained by rotating the given segment by 90° counterclockwise and clockwise about one endpoint, examples and step by step solutions, Common Core Geometry

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### Lines That Pass Through Regions (examples, solutions, videos, worksheets, homework, lesson plans)

Lines That Pass Through Regions, Given two points in the coordinate plane and a rectangular or triangular region, students determine whether the line through those points meets the region, examples and step by step solutions, Common Core Geometry

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### Finding Systems of Inequalities That Describe Triangular and Rectangular Regions (examples, solutions, videos, worksheets, homework, lesson plans)

Finding Systems of Inequalities That Describe Triangular and Rectangular Regions, describe rectangles (with edges parallel to the axes) and triangles in the coordinate plane by means of inequalities, examples and step by step solutions, Common Core Geometry

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### Searching a Region in the Plane (examples, solutions, videos, worksheets, homework, lesson plans)

Searching a Region in the Plane, Visualize cross-sections of three-dimensional objects, how a 3D printer works and its relation to Cavalieri’s principle, examples and step by step solutions, Common Core Geometry

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