Concept Maps

Where there is a blank, you will have to refer to the hard copies in class to get the Key Learning and Unit Essential Questions as they will not copy over to the webpage.  These must be included for the map to be complete.  Remember that for the extra credit grade to be earned, you must choose 3 LEQ's and answer each of them with a complete sentence. 

Title:              Introduction: points, lines and planes     

Unit Essential Question(s): Why are points, lines, and planes considered the building blocks of Geometry?  How can you describe the attributes of a segment?  How can you describe the attributes of an angle?

Key Learning(s): The students must know & use the midpoint and distance formulas.

 

Concept: Nets	Concept: Points, lines, & planes	Concept: Measuring Segments
Lesson Essential Questions: Why is it useful to make nets of 3 dimensional figures?	Lesson Essential Questions: How do you name points, lines, segments, & rays?	Lesson Essential Questions: How do you find & compare lengths of segments?
Vocabulary: net	Vocabulary: Point, line, plane, segment, ray, collinear points, coplanar points, opposite rays, postulate, intersection	Vocabulary: Distance, midpoint, segment bisector, perpendicular bisector, Segment Addition Postulate

Concept: Measuring  Angles	Concept: Special Angle Pairs	Concept: Midpoint & Distance Formulas
Lesson Essential Questions: How do you find & compare measures of angles?	Lesson Essential Questions: Why is it helpful to use special angle pairs to find angle measures?	Lesson Essential Questions: How are averages used to find the midpoint of a segment? Why is the distance formula helpful/
Vocabulary: Angle, sides, vertex, measure, congruent angles, acute angle, right angle, obtuse angle, straight angle, Angle Addition Postulate	Vocabulary: Adjacent angles, vertical angles, complementary angles, supplementary angles, linear pair, angle bisector,	Vocabulary: Distance formula, midpoint formula

Unit Essential Question(s): How can you make a conjecture and prove that it is true?

Key Learning(s): The students must know the converse, inverse, & contrapositive of a conditional statement.

Title:              Reasoning and Proofs

Concept: Conditional Statements	Concept: Biconditionals & Definitions	Concept: Law of Syllogism & Detachment
Lesson Essential Questions: How are the forms of conditional statements related?	Lesson Essential Questions: How are biconditionals related to definitions?	Lesson Essential Questions: How do you use the Law of Syllogism & Law of Detachment to reach a valid conclusion?
Vocabulary: Conditional, hypothesis, conclusion, negation, converse, inverse, contrapositive, equivalent statements	Vocabulary: Biconditional	Vocabulary: Deductive Reasoning, Law of Syllogism, Law of Detachment

Concept: Proofs in Equations	Concept: Proving angles congruent	Concept:
Lesson Essential Questions: How are algebraic properties useful in Geometry?	Lesson Essential Questions: How do you use angle theorems to solve more complex situations?	Lesson Essential Questions:
Vocabulary: Reflexive Property, Symmetric Property, Transitive Property, 2 Column Proof	Vocabulary: Theorem, Paragraph Proof	Vocabulary:

Unit Essential Question(s): How do you prove that 2 lines are parallel?  How do you prove that 2 lines are perpendicular?

Key Learning(s): Students will be able to explain the relationships between various angles formed by parallel lines & a transversal.

Title:              Parallel and Perpendicular Lines                             

Concept: Lines & Angles	Concept: Properties of Parallel Lines	Concept: Proving Lines Parallel
Lesson Essential Questions: What is true about lines & planes that do not intersect?	Lesson Essential Questions: What is different about the angle pairs that form when a transversal intersects parallel lines?	Lesson Essential Questions: How do you prove 2 lines are parallel?
Vocabulary: Parallel lines, skew lines, parallel planes, transversal, alternate interior angles, consecutive (same side) interior angles, corresponding angles, alternate interior angles	Vocabulary: alternate interior angles, consecutive (same side) interior angles, corresponding angles, alternate interior angles	Vocabulary: alternate interior angles, consecutive (same side) interior angles, corresponding angles, alternate interior angles

Concept: Parallel & Perpendicular Lines	Concept: Parallel Lines & Triangles	Concept:
Lesson Essential Questions: How are parallel & perpendicular lines related?	Lesson Essential Questions: What relationships exist between the interior & exterior angles of triangles?	Lesson Essential Questions:
Vocabulary:	Vocabulary: Exterior angle of a polygon, remote interior angles	Vocabulary:

Title:              Congruent Triangles                                   

Unit Essential Question(s): How do you identify corresponding parts of congruent triangles? How do you show that two triangles are congruent? How can you tell whether a triangle is isosceles or equilateral?

Key Learning(s): Write a full statement of what is essential for students to know and do, representing the most important ideas key to understanding the content.

 

Concept: Congruent Figures	Concept: SSS & SAS ASA & AAS	Concept: CPCTC
Lesson Essential Questions: How do you write a congruence statement?	Lesson Essential Questions: Are there ways to prove triangles congruent without knowing all the of the pieces?	Lesson Essential Questions: How do you use CPCTC?
Vocabulary: Congruent Polygons	Vocabulary: Included Angle, Included Side	Vocabulary:

Concept: Isosceles & Equilateral Triangles	Concept: HL Theorem	Concept: Congruence in Overlapping Triangles
Lesson Essential Questions: What are the properties of Isosceles & equilateral triangles?	Lesson Essential Questions: How is right triangle congruence different from other types of triangle congruence?	Lesson Essential Questions: How do you identify congruence in overlapping triangles?
Vocabulary: Base, legs, vertex angle, base angles	Vocabulary: Hypotenuse, legs	Vocabulary:

Concept: Inequalities in 1 Triangle	Concept: Inequalities in 2 Triangles	Concept:
Lesson Essential Questions: Why are inequalities useful when examining the sides and angles of a triangle?	Lesson Essential Questions: How can you compare 2 triangles that have 2 pairs of congruent sides?	Lesson Essential Questions:
Vocabulary:	Vocabulary:	Vocabulary:

Title:              Polygons and Quadrilaterals                     

Unit Essential Question(s): How can you find the sum of the measures of the angles of a polygon?  How can you classify quadrilaterals?  How are sides & angles useful in determining specials case quadrilaterals?

Key Learning(s): Students will be able to explain the relationships between various angles formed by parallel lines & a transversal.

 

Concept: Interior & Exterior Angles of Polygons	Concept: Properties of Parallelograms	Concept: Proving Parallelograms
Lesson Essential Questions: How do you find the sum of the measures of the interior & exterior angles of a polygon?	Lesson Essential Questions: What do you know about the sides & angles of a parallelogram?	Lesson Essential Questions:How do you can you know that a quadrilateral is a parallelogram?
Vocabulary: Equilateral polygon, equiangular polygon, regular polygon	Vocabulary: Parallelogram, Opposite Sides, Opposite Angles, Consecutive Angles, Diagonals	Vocabulary:

Concept: Rhombuses, Rectangles, & Squares	Concept: Proving Rhombuses, Rectangles, & Squares	Concept: Trapezoids & Kites
Lesson Essential Questions: How are rhombuses, rectangles, & squares related?	Lesson Essential Questions: What do the diagonals tell you about a parallelogram?	Lesson Essential Questions: How is a isosceles trapezoid different from a trapezoid? How are triangles useful in understanding kites?
Vocabulary: Rhombuse, Rectangle, Square	Vocabulary:	Vocabulary: Trapezoid, bases, legs, base angles, isosceles trapezoid, midsegment of a trapezoid, kite

Concept: Polygons in the Coordinate Plane	Concept: Area of Parallelograms & Triangles	Concept: Area of Rhombuses, Trapezoids, & Kites
Lesson Essential Questions: What tools can you use to classify polygons in the coordinate plane?	Lesson Essential Questions: How are the formulas for the areas of parallelograms & triangles related?	Lesson Essential Questions: What do you need to know about trapezoids, rhombuses, & kites in order to find their areas?
Vocabulary:	Vocabulary: Base of a Parallelogram, altitude, height	Vocabulary: Height of a Trapezoid

Title:              Similarity                                           

Unit Essential Question(s): How do you use proportions to find side lengths in similar polygons?  How do you show 2 triangles are similar?  How do you identify corresponding parts of similar figures?

Key Learning(s): Students will be able to prove that triangles are similar and use the concept of corresponding parts of triangles.

 

Concept: Ratios & Proportions	Concept: Similar Polygons	Concept: Proving Triangles Similar
Lesson Essential Questions: Why are ratios & proportions useful?	Lesson Essential Questions: What are similar polygons?	Lesson Essential Questions: What are the different ways to prove that 2 triangles are similar?
Vocabulary: Ratio, extended ratio, proportion,	Vocabulary: Similar Polygons, Extended Proportions, Scale Factor, Scale	Vocabulary: Indirect Measurement

Concept: Similarity in Right Triangles	Concept: Proportions in Triangles	Concept: Perimeter & Area of Similar Figures
Lesson Essential Questions: How is the altitude of a right triangle related to similarity?	Lesson Essential Questions: What relationships occur when triangles are divided within themselves?	Lesson Essential Questions: How can you find perimeters & areas of similar polygons?
Vocabulary:	Vocabulary:	Vocabulary:

Title:              Right Triangles                                 Subject(s):   Geometry                                 Grade(s): 10^th

Unit Essential Question(s): How do find a side length or angle measure in a right triangle?  How do trigonometric ratios relate to similar right triangles?

Key Learning(s): Students will be able to use properties of special right triangles and basic trig ratios to solve right triangles.

 

Concept: Pythagorean Theorem & Converse	Concept: Special Right Triangles	Concept: Trigonometry
Lesson Essential Questions: How can the Converse of the Pythagorean Theorem be used to classify a triangle?	Lesson Essential Questions: Why would you use the properties of special right triangles?	Lesson Essential Questions: How do you use trigonometric ratios to find missing angles?
Vocabulary: Pythagorean Triple	Vocabulary:	Vocabulary: Trigonometric Ratios, Sine, Cosine, Tangent,

Concept: Angles of Elevation & Depression	Concept: Area of Regular Polygons	Concept: Trigonometry & Area
Lesson Essential Questions: How do you use angles of elevation & depression to solve problems?	Lesson Essential Questions: How can you find the area of a regular polygon?	Lesson Essential Questions: How can you use trigonometry to find the area of regular polygons & triangles?
Vocabulary: Angle of Elevations, Angle of Depression	Vocabulary: Radius of a Regular Polygon, Apothem	Vocabulary:

Title:              Three Dimensional Shapes - Surface Area and Volume 

Unit Essential Question(s): How do you find the surface area and volume of a solid?  How do the surface areas and volumes of similar solids compare?

Key Learning(s): Students will be able to describe the effects on volume and/or surface area when the dimensions are changed.

 

Concept: Surface Area of Prisms & Cylinders	Concept: Surface Area of Pyramids & Cones	Concept: Volumes of Prisms & Cylinders
Lesson Essential Questions: How do you find the surface area of prisms & cylinders?	Lesson Essential Questions: How do you find the surface area of pyramids & cones?	Lesson Essential Questions: How do you find the volume of prisms & cylinders?
Vocabulary: Prism, bases, lateral faces, altitude, height, right prism, oblique prism, lateral area, surface area, cylinder, right cylinder, oblique cylinder	Vocabulary: Pyramid, base, lateral faces, vertex, altitude, height, regular pyramid, slant height, lateral area, surface area, cone, right cone	Vocabulary: Volume

Concept: V olumes of Pyramids & Cones	Concept: Surface Area & Volumes of Spheres	Concept: Areas & Volumes of Similar Solids
Lesson Essential Questions: How do you find the volume of pyramids & cones?	Lesson Essential Questions: How do you find the surface area & volume of a sphere?	Lesson Essential Questions: How are the areas & volumes of similar solids related?
Vocabulary:	Vocabulary: Sphere, center, radius, diameter, great circle, circumference, hemispheres	Vocabulary: Similar solids

Title:              Circles                                                 

Unit Essential Question(s): How can you prove relationships between angles & arcs in a circle?  How do you find the equation of a circle in a coordinate plane?

Key Learning(s): Students will be able to use the equation of circles and find the arc length or sector.

 

Concept: Circles & Arcs	Concept: Areas of Circles & Sectors	Concept: Inscribed Angles
Lesson Essential Questions: How is the measure of an arc related to its corresponding central angle?	Lesson Essential Questions: What is the difference between finding the area of circle and a sector of a circle?	Lesson Essential Questions: What are the characteristics of an inscribed angle?
Vocabulary: Circle, center, diameter, radius, congruent circles, central angle, semicircle, minor arc, major arc, adjacent arcs, circumference, arc length, congruent arcs	Vocabulary: Sector of a circle	Vocabulary: Inscribed angle, intercepted arc

Concept: Circles in the Coordinate Plane	Concept:	Concept:
Lesson Essential Questions: What information do you need to write the equation of a circle?	Lesson Essential Questions:	Lesson Essential Questions:
Vocabulary: Standard form of an equation of a circle	Vocabulary:	Vocabulary:

Title:              Transformations and Tesselations                          

Unit Essential Question(s): How can you change a figure’s position without changing its size & shape?  How can you change a figure’s size without changing its shape?  How do you recognize symmetry in a figure?

Key Learning(s): Students will be able to apply transformations in a coordinate plane.

 

Concept: Translations	Concept: Reflections	Concept: Rotations
Lesson Essential Questions: How do you write the rule for a translation in a coordinate plane?	Lesson Essential Questions: What is the relationship between the image & preimage of a line of reflection?	Lesson Essential Questions: How do you draw a rotation of a figure?
Vocabulary: Transformation, translation, preimage, image, isometry	Vocabulary: Reflection, line of reflection	Vocabulary: Rotation, center of rotation, angle of rotation, center of a regular polygon

Concept: Symmetry	Concept: Dilations	Concept: Compositions of Reflections
Lesson Essential Questions: How can you identify the type of symmetry in a figure?	Lesson Essential Questions: How can you draw dilation images of a figure?	Lesson Essential Questions: How can map 2 congruent figures onto each other?
Vocabulary: Symmetry, line symmetry, reflectional symmetry, line of symmetry, rotational symmetry, point symmetry	Vocabulary: Dilation, center, scale factor, enlargement, reduction	Vocabulary: Glide reflection

Concept: Tessellations	Concept:	Concept:
Lesson Essential Questions: How can you identify figures that tessellate and the transformations & symmetry in tessellations?	Lesson Essential Questions:	Lesson Essential Questions:
Vocabulary: Tessellation, glide reflectional symmetry, translational symmetry	Vocabulary:	Vocabulary: