Triangles (congruence, similarity)

• What does triangle congruence mean?

  Two triangles are identical in shape and size
• What must be true for two triangles to be congruent?

  All corresponding angles and sides must be equal
• If triangle ABC is congruent to triangle DEF, what can be said about angle A?

  Angle A equals angle D
• How do corresponding sides relate in congruent triangles?

  They are equal in length
• What are the key terms related to triangle congruence?

  • Triangle congruence
  • Shape
  • Size
  • Corresponding angles
  • Corresponding sides
• What is the definition of triangle similarity?

  Two triangles have the same shape but different sizes
• If triangle ABC is similar to triangle DEF, what can be said about angle A?

  Angle A equals angle D
• What are the theorems for proving triangle similarity?

  1. SSS (Side-Side-Side)
  2. SAS (Side-Angle-Side)
  3. AA (Angle-Angle)
• What is the relationship between corresponding sides in similar triangles?

  They are proportional
• What does the SSS theorem state?

  If three sides of one triangle are proportional to another, they are similar
• What does the SAS theorem state?

  If two sides and the included angle are proportional, they are similar
• What does the AA theorem state?

  If two angles of one triangle are equal to another, they are similar
• What are the applications of triangle congruence and similarity?

  • Architecture: Ensuring symmetry and stability
  • Engineering: Designing bridges and structures
  • Surveying: Measuring and mapping land
• What are the congruence theorems and their conditions?

  1. SSS: 3 sides equal
  2. SAS: 2 sides + included angle equal
  3. ASA: 2 angles + included side equal
• What is the result of the SSS theorem?

  Triangles are congruent
• What is the result of the SAS theorem?

  Triangles are congruent
• What is the result of the ASA theorem?

  Triangles are congruent
• How do congruence theorems help in geometry?

  • They provide methods to prove triangle congruence
  • Essential for accurate calculations and predictions
• What is the name of the concept shown in the image?

  Triangle Congruence

  
• What are the three main triangle congruence criteria?

  • SSS (Side-Side-Side)
  • ASA (Angle-Side-Angle)
  • AAS (Angle-Angle-Side)

  
• What does it mean for two triangles to be congruent?

  They have the same size and shape

  
• How can you use triangle congruence to prove that two triangles are congruent?

  • Show that the corresponding sides are equal (SSS)
  • Show that two angles and one side are equal (ASA)
  • Show that two angles and the included side are equal (AAS)

  
• How do the SSS, ASA, and AAS congruence criteria differ?

  SSS uses 3 sides, ASA uses 2 angles and 1 side, AAS uses 2 angles and 1 side