1 3 points, planes, and lines
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This document provides an introduction to basic geometry concepts including points, lines, and planes. It defines a point as an exact location, a line as extending indefinitely in both directions, and a plane as a flat surface that extends indefinitely in all directions. Examples are given to illustrate each concept, such as a ball being a point on a line or an island surrounded by water indefinitely being a plane. The document also introduces naming conventions for points, lines, and planes and describes intersections between these concepts, such as two lines intersecting at a single point.
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2.1 graphing integers on a number line lesson
- A number line is a line with evenly spaced marks that represent numbers like integers, fractions, and other quantities.
- Numbers can be graphed on a number line by placing a point at the mark corresponding to the number.
- Movement right on the number line represents increasing or positive numbers, while movement left represents decreasing or negative numbers.
2.1 graphing integers on a number line lesson
- A number line is a line with evenly spaced marks that represent numbers like integers, fractions, and other quantities.
- Numbers can be graphed on a number line by placing a point at the mark corresponding to the number.
- Movement right on the number line represents increasing/positive numbers, while movement left represents decreasing/negative numbers.
1.2 order of operations lesson
The document discusses the order of operations, known as PEMDAS or P.E.M.D.A.S. It states that PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction and is the proper order to follow when evaluating mathematical expressions. Following PEMDAS is important to get the correct solution and avoid mistakes. Examples are provided to demonstrate how to use PEMDAS to simplify expressions step-by-step.
1.1 writing expressions and equations lesson
This document provides an introduction to expressions and equations in algebra. It defines expressions as statements that do not contain an equals sign, such as 2x - 4, while equations are statements that do contain an equals sign, such as 4n + 7 = 11. The lesson explains that students will practice writing verbal expressions and equations from algebraic forms, and vice versa. It provides examples and emphasizes using words like "more than", "less than", and "times" rather than symbols like "+" and "-".
13 4 tangent ratio lesson
This document discusses using tangent ratios to determine side lengths in right triangles. It defines tangent ratios as the ratio of the length of the opposite leg to the length of the adjacent leg. Tangent ratios can be used to find the measure of distances that are difficult to measure directly. The tangent inverse function, denoted Tan-1, can be used to find a missing angle measure when two sides of a triangle are known. Examples demonstrate setting up and solving tangent ratios and using the tangent inverse to find missing angle measures.
14 5 segment measures lesson
1) The document discusses finding measures of angles formed by chords, secants, and tangents of circles. It provides theorems for calculating angle measures based on intercepted arc lengths.
2) Formulas are presented for calculating lengths of segments associated with circles, including secants, chords, and tangents.
3) Examples demonstrate using the theorems and formulas to find missing angle measures and segment lengths in various circle geometry problems involving combinations of secants, chords and tangents.
14 4 secant-tangent angles
Secant-tangent angles are formed when a secant line intersects a tangent line either on or outside of a circle. If the vertex is outside the circle, the degree measure is half the difference between the intercepted arcs. If the vertex is on the circle, the degree measure is half the intercepted arc. When two tangent lines form an angle, the degree measure is also half the difference between the intercepted arcs.
14 3 secant angles lesson
This document discusses secants, tangents, and the angles they form in relation to circles. It states that a secant line intersects a circle at two points, and if two secants intersect inside a circle, the measure of the angle formed is half the sum of the intercepted arcs. The document provides examples of finding measures of interior and exterior angles formed by secants and tangents, as well as measures of intercepted arcs. Students are expected to apply the concepts to solve problems involving angles and arcs formed by secants and tangents intersecting inside, outside, and on the circumference of circles.
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1 3 points, planes, and lines
- 1. POINTS, LINES ANDPOINTS, LINES AND PLANESPLANES Jim Smith JCHSJim Smith JCHS Section 1-1Section 1-1
- 2. What is Geometry?What is Geometry? Geometry is the study of shapesGeometry is the study of shapes They studied Geometry in AncientThey studied Geometry in Ancient Mesopotamia & Ancient EgyptMesopotamia & Ancient Egypt Geometry is important in the art andGeometry is important in the art and construction fieldsconstruction fields
- 3. POINTPOINT AA POINTPOINT is an exact location onis an exact location on a graph, shape or in space.a graph, shape or in space. The ball is aThe ball is a POINTPOINT on the line.on the line.
- 4. LINELINE AA LINELINE goes in opposite directionsgoes in opposite directions and never, ever ends.and never, ever ends. Take a pearlTake a pearl necklacenecklace and stretch it out.and stretch it out. The pearls are like points on a line.The pearls are like points on a line.
- 5. PLANEPLANE AA PLANEPLANE is a flat surface thatis a flat surface that goes on forever in all directions.goes on forever in all directions. Imagine sitting on an island in theImagine sitting on an island in the middle of the ocean. No mattermiddle of the ocean. No matter which way you look…all you seewhich way you look…all you see is water…forever.is water…forever.
- 6. TO NAME A POINT- WE USETO NAME A POINT- WE USE A CAPTIAL LETTERA CAPTIAL LETTER .A.A .X.X
- 7. TO NAME A LINE- USE ANY 2TO NAME A LINE- USE ANY 2 POINTS ON THE LINEPOINTS ON THE LINE LINE RT or LINE ST orLINE RT or LINE ST or LINE RSLINE RS R T S RT RS
- 8. POINTS ON THE SAME LINE ARE CALLED COLLINEAR POINTS A, B, AND Y AREA, B, AND Y ARE COLLINEARCOLLINEAR A Y B.. .. ..
- 9. TO NAME A PLANE WE USE 3TO NAME A PLANE WE USE 3 OR 4OR 4 NONCOLLINEARNONCOLLINEAR POINTSPOINTS PLANE WAG or XAG or WXAPLANE WAG or XAG or WXA .A.W . PLANES CAN BE NAMED USING 1 LETTER …. PLANE Q Q X .G
- 10. THETHE INTERSECTIONINTERSECTION OFOF 2 LINES IS A POINT2 LINES IS A POINT s S IS THE INTERSECTIONINTERSECTION OF THE 2 LINES
- 11. LINE AB IS CONTAINED INLINE AB IS CONTAINED IN PLANEPLANE QQ Q A B
- 12. LINE XYLINE XY INTERSECTSINTERSECTS PLANEPLANE QQ AT POINT XAT POINT X Q X Y .
- 13. THE ARROW INTERSECTSTHE ARROW INTERSECTS THE TARGET AT 1 POINTTHE TARGET AT 1 POINT
- 14. Lines YB and XZLines YB and XZ do notdo not intersectintersect X Y B ZZ .. .
- 15. THE INTERSECTION OF 2THE INTERSECTION OF 2 PLANES IS APLANES IS A LINELINE A C E F G B C H D EE GG
- 16. YY W. S. P XX G. POINTS AND LINES CONTAINED INPOINTS AND LINES CONTAINED IN THE SAME PLANE ARE CALLEDTHE SAME PLANE ARE CALLED COPLANARCOPLANAR