Chapter 1: Basics of Geometry
... If A(x1, y1) and B(x2, y2) are points in the coordinate plane, then the distance between A and B is ...
... If A(x1, y1) and B(x2, y2) are points in the coordinate plane, then the distance between A and B is ...
Chapter 4 Euclidean Geometry
... Definition 4.14 A convex quadrilateral 3ABCD is called a parallelogram if the opposite sides AB, CD and BC, AD are parallel. A Rhombus is a parallelogram having two adjacent sides congruent. A square is a rhombus having two adjacent sides perpendicular. Theorem 4.15 A diagonal of a parallelogram div ...
... Definition 4.14 A convex quadrilateral 3ABCD is called a parallelogram if the opposite sides AB, CD and BC, AD are parallel. A Rhombus is a parallelogram having two adjacent sides congruent. A square is a rhombus having two adjacent sides perpendicular. Theorem 4.15 A diagonal of a parallelogram div ...
Two-Dimensional Figures
... are all segments. A polygon’s sides intersect exactly two other sides, but only at their endpoints. Examples: ...
... are all segments. A polygon’s sides intersect exactly two other sides, but only at their endpoints. Examples: ...
Quadrilaterals and polygons
... If you are working with a regular polygon, you can determine the size of EACH exterior angle by simply dividing the sum, 360, by the number of angles. Remember, this will ONLY work in a regular polygon. Example: What is the size of one of the exterior angles of a regular pentagon? ...
... If you are working with a regular polygon, you can determine the size of EACH exterior angle by simply dividing the sum, 360, by the number of angles. Remember, this will ONLY work in a regular polygon. Example: What is the size of one of the exterior angles of a regular pentagon? ...
Geometry Standards with Learning Targets
... (CCSS: G.SRT.9, G.SRT.10, G.SRT.11; 6-8 days) Students will be able to: a) Derive the formula A = (1/2)absin C and be able to apply the formula to compute the area of a triangle. b) Understand the derivation of the Law of Sines and be able to apply the Law of Sines to find unknown measurements in ri ...
... (CCSS: G.SRT.9, G.SRT.10, G.SRT.11; 6-8 days) Students will be able to: a) Derive the formula A = (1/2)absin C and be able to apply the formula to compute the area of a triangle. b) Understand the derivation of the Law of Sines and be able to apply the Law of Sines to find unknown measurements in ri ...
Geometry Concepts VOCABULARY
... Chapter 9 Image: when a transformation moves or changes a figure in some way to produce a new figure. Preimage: another name for the original figure. Isometry: a transformation that preserves length and angle measure. Vector: is a quantity that has both direction and magnitude, or size. Initial Poin ...
... Chapter 9 Image: when a transformation moves or changes a figure in some way to produce a new figure. Preimage: another name for the original figure. Isometry: a transformation that preserves length and angle measure. Vector: is a quantity that has both direction and magnitude, or size. Initial Poin ...
Activities 1
... Show that you need 6 line segments to join each point to every other point when there are 4 non-collinear (not on same straight line) points. ...
... Show that you need 6 line segments to join each point to every other point when there are 4 non-collinear (not on same straight line) points. ...
topic 11 triangles and polygons
... This means that the interior angles that surround a point have to sum to 360 exactly. For example, four squares can surround a point. Since each square has an interior angle with measure 900, then the sum of four of these with be exactly 3600. It is also true that two regular octagons and one square ...
... This means that the interior angles that surround a point have to sum to 360 exactly. For example, four squares can surround a point. Since each square has an interior angle with measure 900, then the sum of four of these with be exactly 3600. It is also true that two regular octagons and one square ...
Section 9.1- Basic Notions
... • A simple closed surface has exactly one interior, has no holes, and is hollow. It separates space into interior, surface, and exterior. • A sphere is the set of all points at a given distance from a given point, the center. • A solid is the set of all points on a simple closed surface along with a ...
... • A simple closed surface has exactly one interior, has no holes, and is hollow. It separates space into interior, surface, and exterior. • A sphere is the set of all points at a given distance from a given point, the center. • A solid is the set of all points on a simple closed surface along with a ...
the size-change factor
... Similar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship. ...
... Similar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing of this ship the actual size of the ship. ...
0002_hsm11gmtr_0601.indd
... 1. A polygon that has an interior angle greater than 180° is a __________ polygon. 2. A polygon that has no interior angles greater than 180° is a ___________ polygon. ...
... 1. A polygon that has an interior angle greater than 180° is a __________ polygon. 2. A polygon that has no interior angles greater than 180° is a ___________ polygon. ...
Similar Polygons
... Lesson Focus This lesson introduces one of the major topics in geometry, the study of similar figures. Congruent figures have the same size and shape. Similar figures have the same shape. ...
... Lesson Focus This lesson introduces one of the major topics in geometry, the study of similar figures. Congruent figures have the same size and shape. Similar figures have the same shape. ...
Chapter 1
... In general, we classify polygons by the number of sides they have. A polygon with n sides is an n-gon. ...
... In general, we classify polygons by the number of sides they have. A polygon with n sides is an n-gon. ...
File
... Draw a ray and label the endpoint B and another point on the ray A. Place the protractor so the middle of the bottom edge is over the endpoint of the ray. Find the 0 mark on the protractor and place a point. Label it C. Draw ray BC. ...
... Draw a ray and label the endpoint B and another point on the ray A. Place the protractor so the middle of the bottom edge is over the endpoint of the ray. Find the 0 mark on the protractor and place a point. Label it C. Draw ray BC. ...
Unit 9_Basic Areas and Pythagorean theorem
... The apothem of a regular polygon is the line from the center to the midpoint of a side. The radius is the distance from the center to any vertex. By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides. ...
... The apothem of a regular polygon is the line from the center to the midpoint of a side. The radius is the distance from the center to any vertex. By definition, all sides are the same length, so the perimeter is simply the length of a side times the number of sides. ...
GEO B Unit 7 PowerPoint
... Finding the Number of Sides • By knowing the measurement of one interior angle of a regular polygon, we can determine the number of sides of the polygon as well. • How? – Since we know that all angles are going to have the same measure we will multiply the known angle by the number of sides of the ...
... Finding the Number of Sides • By knowing the measurement of one interior angle of a regular polygon, we can determine the number of sides of the polygon as well. • How? – Since we know that all angles are going to have the same measure we will multiply the known angle by the number of sides of the ...
Regular polytope
In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians.Classically, a regular polytope in n dimensions may be defined as having regular facets [(n − 1)-faces] and regular vertex figures. These two conditions are sufficient to ensure that all faces are alike and all vertices are alike. Note, however, that this definition does not work for abstract polytopes.A regular polytope can be represented by a Schläfli symbol of the form {a, b, c, ...., y, z}, with regular facets as {a, b, c, ..., y}, and regular vertex figures as {b, c, ..., y, z}.