Katie Blumenstock

G.1.3.1: Use properties of congruence,
correspondence, and similarity in problemsolving settings involving two- and threedimensional figures.
◦ G.1.3.1.2: Identify and/or use proportional relationships
in similar figures.

G.1.3.2: Write formal proofs and/or use logic
statements to construct or validate arguments
◦ G 1.3.2.1: Write, analyze, complete, or identify formal
proofs (e.g. direct and/or indirect proofs/proofs by
contradiction)
Recall the information from the previous
section such as “If-then” statements, the
conclusion and hypothesis, deductive
reasoning.
 Equality
◦ AB=AB
◦ m∠A = m∠A
 Congruence
◦ AB ≅ AB
◦ ∠A ≅ ∠A

Look at it as though you are looking at yourself in
the mirror. Picture the mirror as the equal sign.
You are on one side but you are also on the other
 Equality
◦ If AB=CD, then CD= AB
◦ If m∠A=m∠B, then m∠B=M∠A
 Congruence
◦ If AB ≅ CD, then CD ≅AB
◦ If ∠A ≅ ∠B, then ∠B ≅ ∠A

Flip –Flop. If I say that Matt is as tall as George.
Can I say that George is as tall as Matt?

Equality

Congruence

◦ If AB = CD and CD = EF, then AB = EF
◦ If m∠A = m∠B and m∠B=M∠C, then m∠A=
m∠C
◦ If AB ≅ CD and CD ≅ EF, then AB ≅EF
◦ If ∠A≅∠B and ∠B ≅ ∠C, then ∠A≅∠C
Bring them up to the front. 3 people that are
around the same height. If I say that Matt is as
tall as George and Matt is as tall as Ray. Can I
say that George is as tall as Ray?
What is the difference?
◦ Equality always deals with numbers
◦ Congruence always deals with the
actual angles
 Remember:
RST --- 123
◦ Reflexive comparing 1 component
◦ Symmetric comparing 2 components
◦ Transitive comparing 3 components
Complete the following exercise.
∠1 and ∠2 are vertical angles and ∠2 ≅ ∠3.
Show that
∠1≅ ∠3.
∠1 ≅ ∠2 Vertical Angles Theorem
∠2 ≅ ∠3 Given
∠1 ≅ ∠3 Transitive Property of Congruence
Create Your
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