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Master the Pythagorean Theorem: Applications and Examples

Geometry: Master Shapes, Proofs & Spatial Reasoning

Angles and Lines

Angle relationships

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

Perpendicular bisectors

Angle bisectors

Angle Bisectors

Coordinate Plane

Cartesian plane

Cartesian Plane — Coordinates

Draw on coordinate planes

Triangles

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Classifying Triangles

Isosceles and Equilateral Triangles

Circles

Angles in a circle

Chord properties 

Tangent properties

Circles and circumference 

Circle properties

Arcs of a circle

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

Surface Area and Volume

Volume of rectangular prisms word problems

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Introduction to volume

Calculate the Volume

Volume of prisms

Find the volume

Volume of Prisms Calculate Area and Volume

Rectangular Prisms Table

Volume of Prisms — Word Problem

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area of cylinders

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Transformations

Identifying vertices

Line symmetry

Rotational symmetry and transformations

Understanding tessellations

understand tessellations Interior Angle

Tessellations using translations and reflections

tessellations using translations and reflections

Tessellations using rotations

Introduction to transformations

Horizontal and vertical distances

Similarity

Similar solids

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Congruence

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Logic

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

Biconditionals

Deductive reasoning

Algebraic proofs

Reasoning

Consecutive integers

Number sequences

Finding the missing digit

math

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Intro

In the previous section, we have learned the Pythagorean Theorem. We will now apply the knowledge to answer questions involving compound polygons.

Using the Pythagorean Relationship in math

Squares and square roots

Estimating square roots