# Geometry

Selected questions

## Points, Lines, and Planes

Discover the difference between in geometric elements: points, lines, segments, rays, and planes. Learn to read geometry syntax and apply it to figures. Use basic geometry to solve for lengths and areas.

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## Geometric Logic

Introduce yourself to logical statements, essential components for completing proofs. Utilize logical operators to synthesize sound statements and also provide their opposites.

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## Angles

Before learning about geometric figures, discover a new form of measuring rotational distance between segments: angles. Discover classifications, measurements, and manipulations based on notation and graphical representations. Differentiate supplementary, complementary, and congruent angles and use their properties to solve for unknown angles.

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## Triangles

Explore the simplest polygon: the triangle. Learn about the different types, their common attributes, and the applied concepts of right triangles: the Pythagorean Theorem, special right triangles, trigonometry, and the area formula. Congruence and similarity of triangles are presented and integrated throughout the unit. Application of concepts is enforced.

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## Polygons

Expand your understanding of all types of polygons and their properties. Apply the properties of side numbers, internal and external angles, and polygon area to help solve unknown lengths, areas, and angles in a range of challenging problems.

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## Circles

The universe's setpiece, the form that nature seeks and achieves: the circle. Explore the different aspects, known constants, and equations for the simple shape. Combined with knowledge of triangles, this will serve as a launch pad into trigonometry.

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## Vectors

Vectors are line segments with directionality, and can be very helpful, for example, in physics, to demonstrate force diagrams. You will practice annotating, graphing, analyzing, and combining vectors to help prepare for trigonometry.

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## Surface Area and Volume

Add another dimension to polygons and spatially visualize 3-dimensional figures. Apply naming conventions and calculate surface area using your base knowledge of simple polygons. These equations also will help you find the volume of simple shapes. Once mastered, these volume equations are a stepping stone into finding the volume of more complex shapes using calculus.

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## Transformations

Using a coordinate plane, transform points, planes, or functions using symmetry, reflection, rotation, and translation. Continue to challenge your visual and spatial intelligence in these practice questions.

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