Download Geometry Level 7

Academy of Math
Geometry – Level 7 Guided Notes In this activity you will be working with lines, angles, polygons, motion geometry, rotational symmetry and tiling patterns 1. There are different kinds of lines: A _______________ is a straight line with two endpoints A ________is part of a line that goes in one direction starting from a single endpoint A ________goes in both directions without endpoints 2. Line segments, Rays, and Lines can be______________, they go from side to side OR they can be___________, they go up and down An ________ Line is neither horizontal nor vertical 3. When line segments cross we say they intersect The point at which they intersect is called the point of intersection When intersecting lines form a square corner or right angle they are called __________ Lines that travel in the same direction and never meet or change their distance from one another are called ____________ When lines are parallel they are marked with arrows 1 A _____________ Line is a straight line segment that joins opposite corners on a polygon When lines are equal in length, they are marked with small dashes 4. __________are formed when two lines share one endpoint Line segment AB and line segment BC share the endpoint B The shared endpoint is called the ___________ When naming an angle the vertex letter is always in the middle, this is angle ABC 5. Angles are measured and drawn by a ____________which uses units called __________(o) When an angle forms a square corner it is called a _________ Angle; a right angle measures 90o A __________ Angle measures 180o An _________ Angle measure less than 90o An ________ Angle measures greater than 90o but less than 180o 2 6. ___________ Angles: angles formed by intersecting lines have a common vertex and the angles that are opposite to one another are always congruent Angle CFB and angle EFG are Opposite Angles and are the same size and shape Angle CFE and angle BFG are also opposite angles and the same size and shape 7. _____________ Angles: the ones next to each other formed by intersecting lines always equal 180o Since angle EFB = 180o then the sum of angle EFT and angle EFG must also equal 180o Here’s another example, if angle FYZ equals 60o, what does angle KYX measure? Subtract 60o from 180o Angle KYX measures 120o 3 8. A __________is a closed figure formed by line segments Polygons are named but the number of sides they have: A three‐sided polygon is a __________ A four‐sided polygon is a ________________ A five‐sided polygon is a ______________ A six‐sided polygon is a ____________ When a polygon is formed by line segments of equal length and when all of its angles are equal in size, the polygon is considered a __________ Polygon 9. ______________is when figures have the same size and shape These figures are all identical in size and shape so these figures are congruent If the figures are the same shape but different sizes they are __________but not congruent 10. A line that divides one figure into two congruent parts is called a Line of ______________ The line must go through the figure so that each part looks the same on both sides of the line This is a line of symmetry since both parts of the circle are congruent 4 Some polygons do not have a line of symmetry and there is no way of making two congruent parts from the whole 11. Angles are sometimes used to name types of triangles *Remember that a triangle is a three‐sided polygon A __________‐Angled Triangle has one 90o angle An ____________‐Triangle has three equal sides A __________‐Triangle has three unequal sides An ___________‐Angled Triangle has one angle greater than 90o but less than 180o An _________‐Angled Triangle has all three angles measuring less than 90o Whatever the shape of the triangle, the sum of the angles always equals 180o 12. Triangles can also be named based on the nature of the triangle sides An __________‐Triangle has two equal sides 5 13. _______________are polygons formed by line segments that have 4 sides and are named by the number or pairs of parallel sides Whatever the shape of the polygon, the sum of the angles always equals 360o Squares and Rectangles are special quadrilaterals: __________have all four sides the same length and all four corners are right angles ____________have two pairs of equal sides and all four corners are right angles ______________: each pair of opposite sides is equal in length and parallel ____________: a parallelogram with four equal sides ___________: two sides are parallel _______: two pairs of sides that are next to each other are equal 14. Geometry that describes the movement of congruent figures is called __________ Geometry In motion geometry a figure can _______to create a congruent image All points on the slide image are the same distance from the matching points on the original image The _____________shows the direction of the slide motion The direction of the slide can be up, down, left, or right This image has moved down two spaces and to the right six spaces The rule that describes the motion of the slide is D2; R6 A figure can _______ to create a congruent image 6 All points in the flip image are the same distance from the flip line as the original figure but on the opposite side of the line A figure can also ______ to create a congruent image All points on the turn image are turned on the same angle from the same point called the ___________________ Turns are measured as ¼ turns, ½ turns, ¾ turns and full turns A figure can turn in a ____________direction (cw), the same direction as the hands on a clock or in a ____________direction (ccw), the opposite direction as a clock Any figure that fits onto itself in less than full turn has ___________Symmetry or _______ Symmetry If I turn this square one quarter turn clockwise the turn image perfectly maps to the original square If I turn it ½ turn the turn image maps again It maps again with a ¾ turn and with a full turn The square maps onto itself 4 times in one full turn The square’s order of ___________ symmetry, the number of times it maps on itself is 4 Here’s another example using an equilateral triangle How many times with the triangle map on itself within one full turn An equilateral triangle’s order of rotational symmetry is 3 15. Using your knowledge of different polygons you are able to fit together geometric shapes so that they completely cover a surface with no gaps or overlaps, this is called _________ 7 A ________________is a tiling pattern that uses one congruent regular polygon *Remember that congruent means that the shapes are all the same size and that a regular polygon has sides all the same length These are tessellation examples: 8 Word Bank Protractor Clockwise Rotational Symmetry Right Angle Equilateral Straight Angle Vertex Adjacent Angles Acute Angle Turn Symmetry Obtuse Angle Line Segment Oblique Line Diagonal Line Turn Center Scalene Ray Opposite Angles Horizontal Polygon Quadrilaterals Vertical Line Intersect Angles Slide Arrow Quadrilateral Line of Symmetry Tessellation Pentagon Congruency Parallelogram Degrees Perpendicular Parallel Squares Isosceles Motion Geometry Rectangles Rhombus Similar Hexagon Trapezoid Slide Tiling Kite Regular Polygon Vertex Flip Turn Counter Clockwise Right Obtuse Acute 9