Circle theorems
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Euclidean Geometry is another critical branch of mathematics. It weighs a lot of marks in high school math, and teachers need to teach the concept with care and inclusivity.
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Radian and Degree Measure ppt.pptx
This document discusses measuring angles in degrees and radians. It defines an angle, describes quadrant classification of angles, and conversions between degree and radian measure. Key concepts covered include: one radian is the measure of a central angle that intercepts an arc equal to the radius; to convert degrees to radians multiply by π/180; to convert radians to degrees multiply by 180/π.
Mathematics Form 1-Chapter 8 lines and angles KBSM of form 3 chp 1 ...
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Obj. 45 Circles and Polygons
The student is able to develop and use formulas to find the areas of circles and regular polygons. Key formulas include using π to find the circumference and area of a circle based on diameter or radius. For regular polygons, the student can find the area using the apothem and perimeter, or use special formulas for equilateral triangles (s2/3/4) and regular hexagons (6s2/3/4).
Areas related to Circles - class 10 maths
This a ppt which is based on chapter circles of class 10 maths it is a very good ppt which will definitely enhance your knowledge . it will also clear all concepts and doubts about this chapter and its topics
Chapter 9 plane figures
- A triangle is a three-sided polygon with three angles that sum to 180 degrees. Triangles can be classified based on side length (scalene, isosceles, equilateral) or angle type (acute, right, obtuse).
- The triangle inequality theorem states that any side of a triangle must be less than the sum of the other two sides and greater than the difference of the other two sides.
- A quadrilateral is a four-sided polygon. Quadrilaterals can be simple or complex, and simple ones can be convex or concave. The interior angles of any simple quadrilateral sum to 360 degrees.
- A circle is the set of all points in a plane equid
Geom11 Whirwind Tour
This document provides an overview of key concepts for calculating the areas of polygons and circles. It discusses how to find the sum of interior angles for polygons by dividing them into triangles, and how to calculate the apothem to determine the area of regular polygons. It also reviews the formulas for circumference and area of circles, as well as calculating arc length and sector area as proportions of the total circumference and total circle area.
Flashcards - Quantitative Review.ppt
The document provides information about various geometry concepts related to polygons, triangles, circles, coordinate planes, and their properties and relationships. It includes formulas and explanations for calculating sums of interior angles of polygons, areas of different shapes, lengths of arcs and sectors, slopes and intercepts of lines, distances between points, and intersections of lines. Examples are provided to demonstrate applying these concepts to solve geometry problems.
Angles, Right Triangle, Pythagorean Theorem, Trigonometric Ratios
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Circle theorems
- 1. Draw and label on a circle: Centre Radius Diameter Circumference Chord Tangent Arc Sector (major/minor) Segment (major/minor)
- 2. a a 180 - 2a r r Circle Fact 1. Isosceles Triangle Any triangle AOB with A & B on the circumference and O at the centre of a circle is isosceles.
- 3. Circle Fact 2. Tangent and Radius The tangent to a circle is perpendicular to the radius at the point of contact.
- 4. Circle Fact 3. Two Tangents The triangle produced by two crossing tangents is isosceles.
- 5. Circle Fact 4. Chords If a radius bisects a chord, it does so at right angles, and if a radius cuts a chord at right angles, it bisects it.
- 6. Circle Theorem 1: Double Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.
- 7. Circle Theorem 2: Semicircle The angle in a semicircle is a right angle.
- 8. Circle Theorem 3: Segment Angles Angles in the same segment are equal.
- 9. Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180o .
- 10. Circle Theorem 5: Alternate Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment.
- 11. Circle Theorem 1: Double Angle The angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference.
- 12. a a b b 180 - 2b 180 – 2a 2a + 2b = 2(a + b)
- 13. Circle Theorem 2: Semicircle The angle in a semicircle is a right angle.
- 14. 180 – 2a 180 – 2b a a b b 360 – 2(a + b) = 180 180 = 2(a + b) 90 = (a + b)
- 15. Circle Theorem 3: Segment Angles Angles in the same segment are equal.
- 16. a a 2a
- 17. Circle Theorem 4: Cyclic Quadrilateral The sum of the opposite angles of a cyclic quadrilateral is 180o .
- 18. a b 2a 2b 2a + 2b = 360 2(a + b) = 360 a + b = 180
- 19. Circle Theorem 5: Alternate Segment The angle between a chord and the tangent at the point of contact is equal to the angle in the alternate segment.
- 20. a 90 - a 90 - a 180 – 2(90 – a) 180 – 180 + 2a 2a a
- 21. Double Angle Semicircle Segment Angles Cyclic Quadrilateral Alternate Segment