Ideas in Geometry/Instructive examples

This page will serve as an index of all problems worked out as instructive examples of the concepts involved in the course Ideas in Geometry/.

List the examples here as links.

Group Examples

Proving the Pythagorean Theorem By Picture/

Pythagorean Theorem Proof by Picture-Leonardo da Vinci Proof

Proving the Area of a Quadrilateral

Proving the Area of a Trapezoid

Proving Parallel Bisectors in Quadrilaterals

Proving Pythagorean Theorem Using Similar Angels

Individual Examples

Section 1.1#3

Section 3.2#7

Section 1.3#19

Section 1.3#21

Finding a Midset (21 from 1.3)

Section 3.2#26

Section 3.2 Number 28

3.2#44

Section 2.1#6

Section 3.1#23

9 from 2.1, Proof by Picture using Venn Diagrams

Problem#22 from Section 1.3, Drawing a Parabola

Section 2.1 Basic Set Theory number 10

Section 2.3 #4

Section 2.4 problem 23

Section 2.1#7

Section 1.2#11

Continued Fractions, Section 3.2#30

Proving Sets Equal, Section 2.1#11

If-Then Truth Tables, Section 2.2#3

Proof by Vienn Diagrams Section 2.1#5

Section 2.2#2

Section 2-3#3 Tessellating Nonregular Hexagons/

Section 2.3#6

Monty Hall Lesson

Section 2.4#14

Section 2.4:#24

Section 2.1#12

Section 3.2 Problem 42 - Lattice Area, Pick's Theorem, and Probability

Section 3.2 Problem 7-Using Brahmagupta's Formula

Section 1.2 problem#17

Lesson 10 logic

Lesson 17- Properties of Triangles

Lesson 15: Tessellations

Lesson 6: Introduction to City Geometry

Lesson 4: Algebraic Geometry

Lesson twenty Eight: Fields

Lesson 1: Euclid's Axioms

Lesson 21: Wacky Dice