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- Geometry

#### Geometry

- Understand the terms - Point, Line, Plane, Collinear Points, Coplanar Points, Segment, Ray, Opposite Rays, Line segments, End points
- Measuring and Constructing Segments - Ruler Postulate
- Constructing and Comparing Congruent segments
- Segment Addition Postulate
- Pairs of Angles - Adjacent angles, Linear Pair, Complementary Angles, Supplementary Angles, Vertical Angles, Adjacent Angles
- Using Midpoint and Distance Formula
- Finding Perimeter and Area of a Quadrilateral on a Coordinate Plane
- Classifying Polygons
- Measuring, Constructing and Classifying Angles
- Naming Angles and Protractor Postulate
- Identifying Congruent Angles
- Angle Addition Postulate
- Bisecting Angles
- Slope: Rate of Change
- Constructions - Perpendicular and Angle Bisectors

- Writing Conditional Statements, Related Conditional Statements, Biconditional Statements.
- Making Truth Tables
- Writing a Conjecture
- Reasoning and using Venn Diagrams
- Inductive Reasoning
- Deductive Reasoning
- Law of Detachment and Law of Syllogism
- Using and Comparing Inductive and Deductive Reasoning
- Postulates - Two Point Postulate, Line Point Postulate, Line Intersection Postulate, Three-point Postulate, Plane-Point Postulate, Plane-Line Postulate, Plane-Intersection Postulate
- Using Inductive Reasoning to make Conjectures
- Theorems - Linear Pair Theorem, Right Angle Congruence, Congruent Supplements Theorem, Congruent Compliments Theorem
- Writing Two-Column Proofs
- Algebraic Properties of Equality and Other Properties of Equality - Reflexive Property, Symmetry property and Transitive Property
- Properties of Congruence - Segment Congruence, Angle Congruence, Symmetric Propertyof Congruence,
- Geometric Relationships - Writing Flowchart Proofs,

- Identifying Lines and Planes - Parallel Lines, Skew Lines and Parallel Planes
- Identifying Parallel and Perpendicular Lines - Parallel Postulate and Perpendicular Postulate
- Angles formed by Transversals
- Properties of Parallel Lines - Corresponding Angles Theorem, Alternate Interior Angles Theorem, Alternate Exterior Angles Theorem, Consecutive Interior Angles Theorem
- Constructing Parallel Lines and Transitive Property of Parallel Lines
- Constructing Perpendicular Lines
- Finding Distance from a Point to a Line
- Linear Pair Perpendicular Theorem, Perpendicular Transversal Theorem,
- Writing Equations of Parallel and Perpendicular Lines
- Partitioning a Directed Line segment and slopes of Parallel and Perpendicular Lines

- Translating a Figure using a Vector
- Writing a Translation Rule
- Translating a figure in the coordinate plane
- Translation Postulate, Composition Theorem and Performing Composition
- Reflections - Reflecting in Horizontal and Vertical Lines, Rules for Reflection
- Reflection Postulate and Performing a Glide Reflection
- Identifying Lines of Symmetry
- Performing Rotations and Coordinate Rules for Rotation about Origin
- Rotation Postulate and Performing Compositions with Rotations
- Identifying Rotational Symmetry
- Dilations and Coordinate Rule for Dilations
- Constructing Dilation and Negative Scale Factor
- Identifying Congruent Figures and Congruent Transformations
- Reflections in Parallel Lines Theorem and Intersecting Lines Theorem
- Performing Similarity Transformations and describing Similarity Transformations
- Proving two figures are similar

- Angles formed by Transversals
- Triangle sum theorem, Exterior Angle theorem
- Using Properties of Congruency to show figures are congruent
- Third Angles Theorem
- Side-Angle-Side Congruence Theorem, Base Angles Theorem
- Side-Side-Side Congruence Theorem, Hypotenuse-Leg Congruence Theorem, Anlge-side-Angle Congruence Theorem, Angle-Angle-Side Congruence Theorem
- Writing Coordinate proofs

- Perpendicular Bisector Theorem and Converse of the Perpendicular Bisector Theorem
- Angle Bisector Theorem and Converse of the Angle Bisector Theorem
- Writing Equations of Perpendicular Bisectors
- Circumcenter of a Triangle - Circumcenter Theorem
- Finding Circumcenter of a Triangle
- Incenter of a Triangle - Incenter Theorem
- Median of a Triangle - Centroid Theorem
- Finding Centroid of a Triangle
- Altitude of a Triangle, Orthocenter and finding orthocenter of a Triangle
- Property of Isosceles Triangles
- Midsegment of a Triangle, Triangle Midsegment Theorem
- Writing Indirect Proofs
- Triangle Longer side theorem, Triangle Larger Angle Theorem, Triangle Inequality Theorem,
- Hinge Theorem and Converse of the Hinge Theorem

- Polygon Interior Angles Theorem and find the sum of the angle measures of a Polygon
- Finding Number of sides of a Polygon and unknown angle measure of a polygon
- Exterior Angle Measures of a Polygon and Polygon Exterior Angles Theorem
- Angle measures in Regular Polygons
- Theorems and Properties of Parallelograms
- Identifying and Verifying Parallelograms
- Proving that Quadrilateral is a Parallelogram
- Properties of special Parallelograms - Rhombus corollary, Rectangle Corollary and Square corollary
- Theorems related to Rhombus - Rhombus Diagonal theorem and This opposite angles theorem
- Theorems related to rectangles - Rectangle Diagonal Theorem
- Properties of Trapezoids
- Theorems related to Isosceles Trapezoids
- Properties of Kites

- Similar Polygons - using similarity statements
- Finding Area and perimeter of similar Polygons
- Proving Triangle similarity by AA - Angle Angle similarity Theorem
- Proving Triangle Similarity by SSS and SAS
- Proving slope criteria using similar triangles
- Proportionality Theorems - Triangle Proportionality Theorem
- Three Parallel lines theorem, Triangle Angle Bisector Theorem

- Pythagorean Theorem and real life problems on the same
- Converse of the Pythagorean theorem
- Pythagorean Inequalities Theorem
- Special Right Triangles and Theorems
- Solving real life problems
- Similar Right Triangles - Right Triangle similarity theorem
- Geometric mean and theorems
- Tangent Ratio and finding tangent ratio
- Solving real life problems with angle of elevation and angle of depression
- Sine and Cosine ratios and sine and Cosine of complementary angles
- Inverse Trigonometric ratios
- Laws of sines and laws of cosines

- Lines and Segments that intersect Circles
- Identifying Special segments and lines
- Coplanar Circles and Common Tangents
- Properties of Tangents and related theorems
- Constructing a Tangent to a Circle
- Finding Arc Measures and Arc Addition Postulate
- Identifying Congruent arcs and Congruent Circles theorem
- Proving Circles are similar
- Chords of Circles and related Chord theorems
- Inscribed Angles and Polygons
- Constructing a Square inscribed in a Circle
- Tangent Segment and Secant Segment
- Circles in the Coordinate Plane
- Writing and Graphing Equations of Circles
- Writing the Standard equation of a Circle
- Writing Coordinate Proofs involving Circles

- Circumference and Area of a Circle
- Measuring Angles in Radians
- Population Density
- Areas of Sectors
- Area of rhombuses, Kites
- Finding Angle Measures in regular Polygons
- Area of Regular Polygons
- Classifying Solids and Describing Cross-sections
- Sketching and Describing Solids of Revolution
- Volumes of Prisms, Pyramids and Cylinders
- Surface area and Volume of Cones
- Surface areas and Volumes of Spheres

- Sample Spaces and Probability
- Independent and Dependent Events
- Two-way tables and Probability
- Probability of Disjoint and Overlapping events
- Permutations and Combinations
- Binomial Distributions

This course on Geometry is designed for high school students who want to gain a strong foundation in various geometric topics and principles. The course will cover topics such as coordinate and spatial geometry, introductory trigonometry, angles, parallel lines, congruent and similar triangles, polygons and other figures, circles, the Pythagorean Theorem, and more. Moreover, the course will also focus on reviewing Algebra skills and developing critical thinking skills through problem-solving and real-world situations.

By the end of the course, students will be able to utilize various geometric tools appropriately, understand and apply geometric theorems, apply geometric concepts in modeling situations, gain a deeper understanding of various Algebra skills, experiment with transformations in the plane, apply trigonometry to general triangles, identify various formulas and use them to solve problems, visualize relationships between two-dimensional and three-dimensional objects, and apply these concepts to real-world situations.

**Click here for a Free Assessment session**

**How Refresh Kid Program works ? **

We follow the US Common Core curriculum, especially as per your School State Standards. Our goals are to

1) Make sure Students understand the concept clearly,

2) Get enough practice to Master the topics.

3) Talk to the Math Teacher during the sessions for any Homework/ Assignment Help.

__Parents usually pick one of these goals:__

1) Catch up to the grade level and give them enough practice so they can perform well in the class.

2) Just align to the class and go a little ahead in the class curriculum

3) Exceeding expectations of the grade level and preparing well for Math Competitions like Math Olympiad, Math League, Noetic Math, AMC8, Math Kangaroo, Math Counts.

We have Monthly Competition within Refresh Kid students in the same level as your child.

**Click here for a Free Assessment session**

** Please Note:** Refresh Kid offers after school math services to help students increase their mastery of the subject. It is important to note that our services are intended to complement and enhance the regular school curriculum, and not to replace it. As such, all students who seek extra help from Refresh Kid are expected to attend and engage in a strong school curriculum. Our services are not a substitute for regular class attendance and participation.