Honors Geometry

Lisa Sova, Dec 14, 2016

Table of Contents

  1. Ch.5
    1. 5.1 - 5.3 Congruent Triangles Thms
    2. 5.7 ITT
  2. Ch.6
    1. Properties of POCs
  3. Ch.7
    1. Largest Angle/Largest Side
    2. Hinge Theorem and Its Converse
    3. Triangle Inequality (II)
  4. Ch.9
    1. 9.1 Transversals
    2. 9.5 Trapezoid Midsegment Thm
    3. 9.5 Trapezoid & Triangle Midsegment Thm
    4. 9.5 Properties of Parallelograms
    5. 9.6 Properties of Isosceles Trapezoids
    6. 9.6 Properties of a Rectangle
    7. Properties of a Rhombus
    8. 9.6 Properties of a Kite
  5. Ch.11 & 17
    1. 11.3 Pythagorean Theorem Converse
  6. Ch.12
    1. 12.2 SSS Similarity
    2. 12.2 AA Similarity
    3. 12.2 SAS Similarity
    4. 12.3 Side-Splitter Theorem
    5. 12.3 Triangle-Angle Bisector Proportionality Theorem
  7. Ch.14
    1. 14.1 Section of Sphere
    2. 14.1 Part 1 Radius Perp. Tangent
    3. 14.2 Part 1 Tangent Perp. Radius Thm
    4. 14.2 Part 2 Perpendicular Bisector of Chord
    5. 14.5.1 Inscribed Angles Thm
    6. 14.5.2 Inscribed Angle Thm
    7. 14.5.3 Cyclic Quadrilaterals
    8. 14.6 Congruent Chords, Arcs, and Central Angles
    9. 14.6 Congruent Chords & Arcs
    10. Circles Secant Lengths
  8. Ch.19
    1. 19.3 Volume of Pyramids
    2. 19.3 Cavalieri's Principle
    3. LA/SA Cylinder
    4. LA/SA Pyramid
    5. LA/SA Prism

1.

Ch.5

  • 1. 5.1 - 5.3 Congruent Triangles Thms
  • 2. 5.7 ITT

1.1.

5.1 - 5.3 Congruent Triangles Thms

Let's see how many different (non-congruent) triangles that we can create given certain circumstances. Move the red dots around to try create different triangles. You can also change the shape of the original triangle, so try changing it's shape. A green triangle represents congruent triangles and orange triangles represent non-congruent triangles.
– Lisa Sova, Eric Smith

1.2.

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2.

Ch.6

  • 1. Properties of POCs

2.1.

Properties of POCs

Explore circumcenters, incenters, centroids and orthocenters.
– Lisa Sova, JDekofsky1

3.

Ch.7

  • 1. Largest Angle/Largest Side
  • 2. Hinge Theorem and Its Converse
  • 3. Triangle Inequality (II)

3.1.

Largest Angle/Largest Side

Drag points A, B, and C to observe the relationship between angle measurements and side lengths.
– Bryan Anderson

3.2.

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3.3.

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4.

Ch.9

  • 1. 9.1 Transversals
  • 2. 9.5 Trapezoid Midsegment Thm
  • 3. 9.5 Trapezoid & Triangle Midsegment Thm
  • 4. 9.5 Properties of Parallelograms
  • 5. 9.6 Properties of Isosceles Trapezoids
  • 6. 9.6 Properties of a Rectangle
  • 7. Properties of a Rhombus
  • 8. 9.6 Properties of a Kite

4.1.

9.1 Transversals

Parallel lines with transversal and non-parallel lines with transversal
– Lisa Sova, Mateusz

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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5.

Ch.11 & 17

  • 1. 11.3 Pythagorean Theorem Converse

5.1.

11.3 Pythagorean Theorem Converse

– Lisa Sova, Rasha Tarek

6.

Ch.12

  • 1. 12.2 SSS Similarity
  • 2. 12.2 AA Similarity
  • 3. 12.2 SAS Similarity
  • 4. 12.3 Side-Splitter Theorem
  • 5. 12.3 Triangle-Angle Bisector Proportionality Theorem

6.1.

12.2 SSS Similarity

This is an applet for you to investigate why SSS Similarity is valid.
– Lisa Sova, G, Mr. Bokar

6.2.

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6.3.

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6.4.

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6.5.

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7.

Ch.14

  • 1. 14.1 Section of Sphere
  • 2. 14.1 Part 1 Radius Perp. Tangent
  • 3. 14.2 Part 1 Tangent Perp. Radius Thm
  • 4. 14.2 Part 2 Perpendicular Bisector of Chord
  • 5. 14.5.1 Inscribed Angles Thm
  • 6. 14.5.2 Inscribed Angle Thm
  • 7. 14.5.3 Cyclic Quadrilaterals
  • 8. 14.6 Congruent Chords, Arcs, and Central Angles
  • 9. 14.6 Congruent Chords & Arcs
  • 10. Circles Secant Lengths

7.1.

14.1 Section of Sphere

This shows cross section of sphere in detail. [br]The section is a circle of radius a. Its area can be found by relating a to the height h and radius of the sphere r.[br]Drag the yellow dot to change the height h.[br]Drag D to turn the marked triangle.
– Lisa Sova, Arthur Lee

7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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8.

Ch.19

  • 1. 19.3 Volume of Pyramids
  • 2. 19.3 Cavalieri's Principle
  • 3. LA/SA Cylinder
  • 4. LA/SA Pyramid
  • 5. LA/SA Prism

8.1.

19.3 Volume of Pyramids

Prove that volume of a pyramid is 1/3 the volume of cube
A pyramid is a polyhedron with one base that is any polygon . Its other faces are triangles.[br][br]The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( in^3,ft^3,cm^3,m^3 , etc). Be sure that all of the measurements are in the same unit before computing the volume.[br][br]The volume V of a pyramid is one-third the area of the base B times the height h.[br][br] V=1/3 * B* h[br]where B is the area of the base and h is the height of the pyramid.Proof of the Formula[br][br]Proof[br][br]In the given figure below[br]   Volume of Cube = Volume of 3 pyramids[br] or Volume of Pyramid=[math]\frac{1}{3}[/math] x Volume of Cube [br] (Cube र Pyramid को base area र उचाई एउटै छ )
Volume of Pyramids (method 1)
Now, Try Yourself as explained above thoroughly.
– Lisa Sova, Bed Prasad Dhakal

8.2.

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8.3.

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8.4.

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8.5.

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