**Geometry**

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Read more about our geometry curriculum, or contact us for more information on our middle school tutoring services today.**Proofs In Algebra**

**Logic**

- Introduction
- Sentence Negations, Conjunctions, Disjunctions
- Conditionals
- Inverse, Converse, Contrapositive
- Bi-conditionals
- Drawing Conclusions
- Sets, Subsets, Set operations
- AlModus Tollens, Law of Chain Rule, Tautology, Syllogism
- Symbolic Logic Proofs
- Error Analysis
- Logic Puzzles

**Points, Lines, Planes and Angles**

- Collinear and non-collinear, Coplanar and

non-Coplanar - Segments, Rays and Distances
- Mid-points, Distance measures and Absolute Values on number lines
- Ruler Postulate, Segment Addition Postulate

- Congruent Segments, Midpoint and bisector of a segment
- Protractor and Angle Addition Postulate
- Overlapping Segments and Angles
- Constructions
- 30

- Congruent, and Adjacent Angles; Bisectors of Angles
- Proving Angles Congruent
- Postulates and Theorems relating Points, Lines, and Planes

**Parallel lines, skew lines and Parallel Planes**

- Theorems on Properties of parallel Lines
- Writing Proofs on Parallel lines
- Proving Lines Parallel; Theorems, Postulates and Proofs
- Drawing Parallel Conclusions
- Algebra of Parallel and perpendicular lines
- Construction of Angle and Perpendicular Bisectors

**Triangles**

- Applying Parallel lines properties to prove “Sum of Angles in a Triangle” theories
- Definitions of Vertex, Mid-points, Bisectors, Angle bisectors, Exterior and Interior Angles in triangles
- Different types of Triangle: Isosceles, Equilateral, Scalene and algebra of their sides and angles
- Bisectors, Medians and Altitudes in Triangles

**Algebra of Straight Lines and Circles**

- Equations of Straight Lines
- Slopes of Parallel and Perpendicular Lines
- Verifying Parallelism and Perpendicularity
- Writing Equations of Parallel and Perpendicular lines
- Equations of Circles: Standard form, Completing the Squares

**Transformations**

- Translations, Rotations, Reflections and their Compositions in rigid systems
- Equations of Lines after translation and reflection
- Congruent Transformations (Isometry)
- Dilations
- Symmetry in figures

**Polygons**

- Interior and Exterior Angles in Regular Polygons
- Applying Parallel lines to Polygons
- Similar Polygons
- Ratio and Proportions
- Algebraic Properties of Proportions
- Similarity in polygons based on ratio-proportion properties

**Similarity in Triangles**

- AA Similarity Postulate
- Theorems for Similar Triangles: SAS, SSS,
- Proportionality Theorem and Angle bisector Theorem in Triangles
- Proving Triangles Similar
- Basic Review of radical operations
- Similarity in Right Triangles and Geometric

Means - Pythagorean Theorem and its Converse
- Basic 3-D Geometry
- Pythagorean in 3-d
- Special Right Triangles
- Basic Trigonometric functions from Right

Triangles

**Inequalities in one and two triangles**

- Algebraic properties of Inequalities
- Exterior Angle Inequality Theorem
- Proving Angle Inequalities in one Triangle
- Inequalities in two Triangles

**Applications of Basic Trigonometric Functions**

- Angles of Elevation and Depression
- Word Problems based on Angles of Elevation and Depression

**Congruency**

- Congruency in Polygons: Corresponding Parts in Congruent Figures
- Proving Triangles Congruent:
- Postulates:
- SSS, SAS, and ASA Postulates

- Theorems:
- General Triangle – AAS
- Right Angled Triangle - HA , LA and LL

- Using Congruency to define relationships among triangles
- Congruencies in Right Angled Triangles
- Congruencies in multiple overlapping Triangles
- Isosceles Triangle Theorem
- Perpendicular Bisector Theorem and its Converse for Triangles
- Angle Bisector Theorem and its Converse for Triangles
- Proving Properties of Medians from Triangle Congruencies
- Congruencies

**Circles**

- Center, Radius, Tangent, Chord, Secant
- Congruent and Concentric Circles
- Inscribed and Circumscribed Polygons
- Tangent Lines Theorems
- Proving Lines are tangent to Circles
- Tangent and Secant lines Theorems
- Tangent Circles, Internal and External Tangencies
- Proving Geometrical Properties based on tangency of Circles
- Arcs of Circles: Minor and Major Arcs
- Congruent Arc Theorems
- Proving Properties based on Congruent Arcs, Tangent Lines and Secant lines
- Theorems on Arcs and Chords
- Proving Congruencies of Arcs and Chords
- Central and Inscribed Angles, Intercepted Arcs, and Theorems based on them
- Intersecting Chords and related Theorems

**Areas and Volumes**

- Areas of Plane Figures
- Areas and Volumes of Solids

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