UNIT 6: Connecting Algebra & Geometry through Coordinates
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1 TASK: Vocabulary UNIT 6: Connecting Algebra & Geometry through Coordinates Learning Target: I can identify, define and sketch all the vocabulary for UNIT 6. Materials Needed: 4 pieces of white computer paper. Pencil, Pen, Markers or Color Pencils. Color is a significant aid here. Vocabulary List (KEY CONCEPTS) Instructions: 1. Fold the 4 pieces of white paper to create 4 flip books (teacher will direct you on folding). As an alternative, the teacher may give you a document to fill in the definitions and sketches of the terms. 2. On the outside cover of the Flip-Book you will write the term VOCABULARY WORD. 3. On the inside of the Flip-Book, there are 2 rectangles for each term. In the first rectangle you will define the term, and in the second rectangle you will sketch a picture of what the term would look like. Use the handout titled KEY CONCEPTS to create the Flip-Book. (You will turn in the handout). Therefore, you will need your Flip-Book to complete this unit and for studying purposes. Key Terms: These terms MUST be in your flip-book. General geometry Coordinate X-intercept Y-intercept Slope Endpoint Lines Line Line Segment Parallel line Perpendicular line Triangles Equilateral Isosceles Scalene Acute Right Angle Obtuse Quadrilaterals Square & Rhombus Rectangle Parallelogram Kite Regular Polygons Pentagon (5 sides) Hexagon (6) Heptagon (7) Octagon (8) Calculations & Theorems Midpoint Distance between two points Pythagorean Theorem
2 NAME DATE: Geometric Figures & Terms Flip Book Project Scoring Reference Max Score Content Complete, Thorough, Accurate 40 Neatness Use of straight edge, legible, presentable 10 Bonus: Creativeness: use of color, use of different lines, notations, additional facts, etc. 5 Scored out of 50 55
3 Coordinate A number used to identify the location of a point. In a plane, there are two coordinates that represent a point, (x,y) Endpoint Slope Y-Intercept X-Intercept
4 Line** A straight arrangement of pts. There are infinitely many points in a line. A line has no endpoints and continues forever in two directions. In analytic geometry, a line in the plane is a set of points whose coordinates satisfy a given linear equation. Denoted by AB Parallel Lines** Coplanar lines that do not intersect The slopes of parallel line are equal to each other, but have a different y-intercept. Denoted by Perpendicular Lines** Most common: Two lines that intersect at a right angle. The slopes of two perpendicular lines are negative reciprocals of each other. Denoted by **From previous flip book
5 ALL Triangle All Triangles: A closed 3-sided figure with three angles The sum of the three interior angles is always 180 Scalene Isosceles Equilateral
6 Area of a Obtuse Acute Right
7 Quadrilateral All Quadrilaterals: A closed 4-sided figure with four angles. Angles can be either convex or concave. In Latin, quadri is a variant of four, and latus means side The sum of the four interior angles is always 360 Area of a Rectangle Rectangle Parallelogram
8 Kite Trapezoid Square Rhombus
9 Pythagorean Theorem Distance** Technically it s the amount of space between two points Interpretation: the shortest amount of space between two points. Midpoint** The EXACT middle point of a line segment. Midpoint Postulate (Euclidian): A line segment has EXACTLY ONE MIDPOINT ** From previous Flip Book
10 Regular polygons. Sides: 3 Name: Equilateral Triangle Each internal : 60 Sides: 4 Name: Square Each internal : 90 Sides: 5 Name: Sides: 6 Name: Each internal : Each internal : Sides: 7 Name: Sides: 8 Name: Each internal : Each internal : Sides: 9 Name: Sides: 10 Name: Each internal : Each internal :
11 KEY Geometric Figures & Terms Flip Book
12 Coordinate A number used to identify the location of a point. In a plane, there are two coordinates that represent a point, (x,y) X-Intercept The point where the graph intersects the X-Axis (when y = 0). Usually in the form (x,0) Y-Intercept The point where the graph intersects the Y-Axis (when x = 0). Usually in the form (0,y) The value of b in the slopeintercept form of a line y = mx + b Slope A measure of steepness of a line. Referred to as the rise over the run Endpoint The point at each end of a line segment or at the beginning of a ray.
13 Line A straight arrangement of points. There are infinitely many points in a line. A line has no endpoints and continues forever in two directions. In analytic geometry, a line in the plane is a set of points whose coordinates satisfy a given linear equation. Denoted by AB Parallel Lines Coplanar lines that do not intersect Parallel Postulate (Euclidian): through a point not on a given line, you can constructed EXACTLY ONE line parallel to the given line. The slopes of parallel line are equal to each other, but have a different y-intercept. Denoted by Perpendicular Lines Most common: Two lines that intersect at a right angle. Euclidean definition: two lines that form congruent adjacent angles (you need to read this definition a couple times to get it) The slopes of two perpendicular lines are negative reciprocals of each other. Denoted by
14 ALL Triangle All Triangles: Three sides & three angles The three angles always add to 180 Equilateral ALL THREE SIDES EQUAL ALL 3 ANGLES ALWAYS 60 Isosceles TWO SIDES EQUAL TWO EQUAL ANGLES Scalene NO SIDES EQUAL NO EQUAL ANGLES
15 Right Has a right angle (90 ) Can be isosceles or scalene Acute ALL angles less than 90 Can be equilateral, isosceles or scalene Obtuse Has an angle more than 90 Can be isosceles or scalene Area of a Three methods to calculate: 1. A = ½ b h 2. ½ a b sin C 3. Heron s formula s (s a) (s b) s c)
16 Quadrilateral A polygon with four sides (edges) and four vertices In latin, quadri is a variant of four, and latus means side Angles can be either convex or concave Sum of the interior angles always equals 360 Parallelogram A special quadrilateral with two sets of parallel lines. Opposite sides are parallel AND equal. Opposite angles are equal; Adjacent angles are supplementary (add to 180 ) Rectangle A special parallelogram with all four interior angles being 90 right angles. Opposite sides are parallel AND equal. All sets of adjacent sides are perpendicular to each other. Area of a Rectangle
17 Rhombus A special parallelogram with all four sides equal to each other. Opposite sides are parallel to each other. Opposite angles are equal to each other. Adjacent angles are supplementary (sum to 180 ). Square A special rhombus with all four sides equal to each other AND all four interior angles being 90 right angles. All sets of adjacent sides are perpendicular to each other Trapezoid A special quadrilateral with one set of parallel lines. Kite A special quadrilateral with two isosceles triangles with the same base.
18 Pythagorean Theorem In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Distance Technically it s the amount of space between two points Interpretation: the shortest amount of space between two points. Midpoint The EXACT middle point of a line segment. Midpoint Postulate (Euclidian): A line segment has EXACTLY ONE MIDPOINT
19 Regular polygons. Sides: 3 Equilateral triangle Each internal angle: 60 Sides: 4 Square Each internal angle: 90 Sides: 5 Regular pentagon Sides: 6 Regular hexagon Each internal angle: 108 Each internal angle: 120 Sides: 7 Regular pentagon Sides: 8 Regular octagon Each internal angle: Each internal angle: 135 Sides: 9 Regular nonagon Sides: 10 Regular decagon Each internal angle: 140 Each internal angle: 144
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