Triangle Congruence

Tibor Marcinek, Aug 29, 2016

Construct these homework proofs and submit your reflection form.

Table of Contents

  1. Explorations
    1. Triangle Congruence Explorations (applet only)
    2. Fishing Rod - SSA case
    3. SSA Exploration - When does the "SSA theorem" hold?
  2. Proofs
    1. SSS proof - ST
    2. ASA proof - ST
  3. Applications
    1. Triangle Congruence Applications - Quadrilateral Properties
    2. Typical Textbook Applications of Triangle Congruence

1.

Explorations

  • 1. Triangle Congruence Explorations (applet only)
  • 2. Fishing Rod - SSA case
  • 3. SSA Exploration - When does the "SSA theorem" hold?

1.1.

Triangle Congruence Explorations (applet only)

Triangle congruence exploration
Is it possible to tell if two triangles (T1 and T2), as described below, are congruent?[br]Explain why they are congruent, not congruent or why it is impossible to tell.[br][br][list][*][i]If you have arrived at a conclusion that two triangle cannot be congruent or it is impossible to tell, use a counterexample to support your argument.[/i][/*][*][i]If you arrived at a conclusion that two triangle must be congruent, either explain it by reference to triangle congruence theorems we had or formulate a new tentative theorem that would capture your observation. [/i][br][/*][/list][br]You may start your exploration by sketching pictures or you can play with the applet below. Make sure you have answers and justification for each question recorded in your notebook.
– Tibor Marcinek

1.2.

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1.3.

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2.

Proofs

  • 1. SSS proof - ST
  • 2. ASA proof - ST

2.1.

SSS proof - ST

– Tibor Marcinek

2.2.

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3.

Applications

  • 1. Triangle Congruence Applications - Quadrilateral Properties
  • 2. Typical Textbook Applications of Triangle Congruence

3.1.

Triangle Congruence Applications - Quadrilateral Properties

– Tibor Marcinek

3.2.

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