Investigating Triangle Congruence Shortcuts

RouquieA, Dec 16, 2022

Table of Contents

  1. Non-Example: SS
    1. Non Example: SS revised
  2. Non-Example: AA
    1. Non-Example: AA
  3. Non-Example: SSA
    1. Non Example: SSA
  4. SAS Theorem
    1. SAS Similarity Theorem AM
  5. ASA Theorem
    1. ASA Theorem AM

1.

Non-Example: SS

  • 1. Non Example: SS revised

1.1.

Non Example: SS revised

The goal of this activity is to determine if we can conclude that two triangles are congruent with only some information about their sides and angles.
What information about the triangles is given?
Identify and perform the transformation that maps C onto F.
Now, identify and perform the transformation that maps B' onto E. Why do the points coincide after the transformation? (Hint: Measure of Angle B'C'E is 62.24 degrees)
Lastly, perform the transformation that SHOULD map A" onto D. Why do the points NOT coincide?
– RouquieA, Catherine, Brian McDermott

2.

Non-Example: AA

  • 1. Non-Example: AA

2.1.

Non-Example: AA

The goal of this activity is to determine if we can conclude that two triangles are congruent with only some information about their sides and angles.
What information about the triangles is given?
Identify and perform the transformation that maps B onto E.
Now, identify and perform the transformation the maps Segment C'B' onto Segment EF. (Hint: The measure of Angle C'B'F is 80 degrees.)
Notice that Point C' and F do not coincide. Why not?
Lastly, perform the transformation that maps Angle B onto Angle E. Notice that the triangles are not congruent.
– RouquieA, Catherine

3.

Non-Example: SSA

  • 1. Non Example: SSA

3.1.

Non Example: SSA

The goal of this activity is to determine if we can conclude that two triangles are congruent with only some information about their sides and angles.
What information about the triangles is given?
Identify and perform the transformation that maps A onto D.
Identify and perform the transformation that maps B onto E. How do you know the points coincide? (Hint: Angle B'A'E measures 60 degrees)
Lastly, perform the transformation that maps Segment A'C' onto Segment DF. Why do C and F NOT coincide?
– RouquieA, Catherine, Brian McDermott

4.

SAS Theorem

  • 1. SAS Similarity Theorem AM

4.1.

SAS Similarity Theorem AM

The goal of this activity is to determine if we can conclude that two triangles are similar with only some information about their sides and angles.
Identify and perform the transformation that maps C onto F.
Identify and perform the transformation that maps Segment B'C' onto EF. (Hint: The measure of Angle B'C'E is 80 degrees.)
Name and perform the transformation that will map A"C" onto FD. Why do you know the sides will coincide?
Lastly, name the transformation that will map A''' onto D and B''' onto E. How do you know the A'''B''' and DE will coincide?
– Catherine, RouquieA, Brian McDermott

5.

ASA Theorem

  • 1. ASA Theorem AM

5.1.

ASA Theorem AM

The goal of this activity is to determine if we can conclude that two triangles are congruent with only some information about their sides and angles.
What information about the triangles is given?
Identify and perform the operation that maps A onto D.
Identify and perform the transformation that maps Segment A'C' onto Segment DF. Why do C and F coincide? (Hint: The measure of Angle C'A'F is 35 degrees.)
Perform the transformation that maps Segment A"B" onto Segment DE. Why do B" and E coincide?
– RouquieA, Brian McDermott

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