Discovering Proportional Parts in Triangles, Parallel Lines

Keri Beechler, Jan 10, 2023

A collection of applets to discover key theorems from 7-4 and 7-5 in Glencoe Geometry book.

Table of Contents

  1. Discovering Proportional Parts in Triangles
    1. 11.6 Triangle Proportionality Theorem
    2. Triangle Midsegment Theorem
  2. Discovering Proportional Parts in Parallel Lines
    1. Parallel Lines Proportionality Theorem
    2. Parallel Lines Congruent Segments Theorem
  3. Discovering Proportional Relationships in Similar Triangles
    1. Corresponding Altitudes and Medians in Similar Triangles
    2. Proportional Angle Bisectors in Similar Triangles
  4. Discovering Triangle Bisector Theorem
    1. Similar Triangles - Angle Bisector

1.

Discovering Proportional Parts in Triangles

7-4, part 1

  • 1. 11.6 Triangle Proportionality Theorem
  • 2. Triangle Midsegment Theorem

1.1.

11.6 Triangle Proportionality Theorem

Use this applet to discover the triangle proportionality theorem!
– tinhel

1.2.

–

2.

Discovering Proportional Parts in Parallel Lines

7-4, part 2

  • 1. Parallel Lines Proportionality Theorem
  • 2. Parallel Lines Congruent Segments Theorem

2.1.

Parallel Lines Proportionality Theorem

Use this applet to discover the parallel lines proportionality theorem![br]How are the ratios of sides AC to CF related to the ratios of sides EB to ED?[br]Move point A and/or point C to explore. [br]Does your conjecture hold true when you drag point A on top of point B to create a triangle?
– mkessler, youngcar, Herholdt Bezuidenhout, tinhel

2.2.

–

3.

Discovering Proportional Relationships in Similar Triangles

7-5, part 1

  • 1. Corresponding Altitudes and Medians in Similar Triangles
  • 2. Proportional Angle Bisectors in Similar Triangles

3.1.

Corresponding Altitudes and Medians in Similar Triangles

Altitudes in similar triangles
Medians in similar triangles
Perimeter in similar triangles
– Keri Beechler, mkessler, allen_flvs

3.2.

–

4.

Discovering Triangle Bisector Theorem

7-5 pt 2

  • 1. Similar Triangles - Angle Bisector

4.1.

Similar Triangles - Angle Bisector

– Thomas Gebbie

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