Congruence statements and corresponding parts

Key notes:

Congruence Statements

  • Congruent Figures: Figures that have the same size and shape are called congruent figures.
  • Congruence Statement: A congruence statement is used to indicate that two figures are congruent.
  • Notation: The symbol ≅ is used to represent congruence.

Example:

  • If triangle ABC is congruent to triangle DEF, it is written as triangle ABC ≅ triangle DEF.

Corresponding Parts

  • Corresponding Parts: When two figures are congruent, their corresponding parts are the parts that match up when the figures are placed on top of each other.
  • Corresponding Sides: Corresponding sides of congruent figures are equal in length.
  • Corresponding Angles: Corresponding angles of congruent figures are equal in measure.

Example:

  • If triangle ABC ≅ triangle DEF, then:
    • AB corresponds to DE
    • BC corresponds to EF
    • CA corresponds to FD
    • Angle A corresponds to angle D
    • Angle B corresponds to angle E
    • Angle C corresponds to angle F

Key Points to Remember:

  • Congruent figures have the same size and shape.
  • Congruence statements are used to indicate that two figures are congruent.
  • Corresponding parts of congruent figures are equal.
  • To write a congruence statement, identify the corresponding vertices and sides of the two figures.

Learn with an example

🔔 Complete the congruence statement.

 Δ EFG ≅  Δ ______ ?

Find the corresponding angles of these congruent shapes.

∠E ≅ ∠J∠F ≅ ∠K∠G ≅ ∠I

Use these corresponding angles, in order, to write a congruence statement.

 Δ EFG ≅  Δ JKI

😀 What are the corresponding parts of the figures below? Select all that apply.

  • D̅E̅ ≅ J̅K̅
  • ∠F ≅ ∠J
  • ∠D ≅ ∠J
  • E̅F̅ ≅ L̅ J̅

Find the corresponding angles of these congruent shapes.

∠D ≅ ∠J∠E ≅ ∠K∠F ≅ ∠L

Find the corresponding sides of these congruent shapes.

D̅E̅ ≅ J̅K̅ E̅F̅ ≅ K̅L̅ F̅D̅ ≅ L̅J̅

There were two correct answer choices:

D̅E̅ ≅ J̅K̅

∠D ≅ ∠J

🔔 Complete the congruence statement.

IJKL ≅ ____

Find the corresponding angles of these congruent shapes.

∠I ≅ ∠R∠J ≅ ∠O∠K ≅ ∠P∠L ≅ ∠Q

Use these corresponding angles, in order, to write a congruence statement.

IJKL ≅ ROPQ

Because these shapes have symmetry, there is more than one correct answer. You could also write:

IJKL ≅ PQRO

Let’s practice!🖊️