Congruence Shortcuts

1
Congruence Shortcuts

• What information do you need to determine if two
  triangles are congruent?
• Do you need all six measurements?
• Are one or two matching measurements enough?
• Are there cases where three measurements will do?
• There are six different combinations of three
  measurements
• Side-side-side (SSS) Three pairs of congruent
  sides
• Side-angle-side (SAS) Two sides and an included
  angle
• Side-side-angle (SSA) Two sides and a
  non-included angle
• Angle-side-angle (ASA) Two angles and an included
  side
• Side-angle-angle (SAA) Two angles and a
  non-included side
• Angle-angle-angle (AAA) Three pairs of congruent
  angles

2
Congruence Shortcuts

• Investigation
• Is SSS a congruence shortcut?
• Step 1
• Construct a triangle with sides of 2, 3, and 4
  inches
• Step 2
• Compare your triangle to those around you. Are
  they congruent?
• C-24 SSS Congruence Conjecture
• If the three sides of one triangle are congruent
  to the three sides of another triangle, then the
  two triangles are congruent.

3
Congruence Shortcuts

• Investigation
• Is SAS a congruence shortcut?
• Step 1
• Construct a triangle with sides of 3 and 4 inches
  with a 40 angle between them
• Step 2
• Compare your triangle to those around you. Are
  they congruent?
• C-25 SAS Congruence Conjecture
• If two sides and the included angle of one
  triangle are congruent to two sides and the
  included angle of another triangle, then the two
  triangles are congruent.

4
Congruence Shortcuts

• Investigation
• Is SSA a congruence shortcut?
• Step 1
• Construct a triangle with sides of 2 and 4 inches
  with a 30 angle not between them
• Step 2
• Compare your triangle to those around you. Are
  they congruent?
• SSA is not a congruence conjecture because it is
  possible to construct more than one triangle with
  the given measurements.