2.4b Triangle Proofs and CPCTC

2.4b Triangle Proofs and CPCTC

Proving Congruent Triangles

FIRST List the given information

NEXT: if any given info includes vocabulary words or parallel lines, WHY is that important? Determine what clue you've been given (use definitions, alt. int. angles etc)

THEN: do you see Reflexive Sides or Vertical Angles?

FINALLY: Determine what postulate will work to show the triangles congruent.

Multiple Choice

Look at this partial proof, Notice the given information. What would be the reason for statment #2?

• Definition of Midpoint

• Definition of congruence

• Transitive Property

• Substitution Property

Multiple Choice

• Reflexive Angles

• Transitive Property

• Definition of Angle Bisector

• Vertical Angles are Congruent

Multiple Select

Use the given info and your prior knowledge to check the 3 statements you would show congruent to prove the triangles congruent.

• $FG\cong FG$

• $\angle DFG\cong\angle EFG$

• $DF\cong EF$

• $DG\cong GE$

• $\angle FGD\cong\angle FGE$

Multiple Choice

Which of the following is a correct statement and reason for the proof shown?

• JK≅KJ

  Symmetric Property

• JK≅JK

  Reflexive Property

• MK≅LJ

  Hypotenuse Congruence

• MJ≅LK

  Midpoint Theorem

Multiple Choice

After listing the Given information, what would be the BEST statement and reason #2?

• $WE≅QE​;\ GE\cong EN$
  
  Definition of Midpoint

• $\angle WEN\cong\angle GEQ$
  Vertical Angles

• $WE≅GE​;\ QE\cong EN$
  Definition Of Midpoint

HL Theorem

Remember SSA is NOT a valid reason to prove triangles congruent.

HOWEVER, in a RIGHT TRIANGLE ONLY, showing corresponding hypotenuse and one pair of corresponding legs will prove the right triangles congruent.

Multiple Choice

If DA is perpendicular to IE, then we can immediately conclude that

• $IA\cong AE$

• $\angle IAD,\ \angle DAE$ are right angles

• $\angle IDA\cong\ \angle EDA$

• $ID\cong ED$

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSA

• AAS

• SAS

• HL

Fill in the Blanks

Which triangle congruence theorem can be used to prove the triangles are congruent?

Fill in the Blanks

Which triangle congruence theorem/postulate can be used to prove the triangles are congruent?

Multiple Select

What additional statements would need to be in the proof to show the triangles are congruent by HL Theorem? (Check all that apply)

• $DN\cong PN$

• $GN\cong GN$

• $m\angle GND\ =90\degree$

• $\angle DGN\cong\angle PGN$

Multiple Choice

∆ABC≅∆XYZ

which is true?

• AB≅XY

• BC≅CB

• AB≅YX

• AB≅XZ

Multiple Choice

∆ABC≅∆XYZ

which is true?

• $\angle C\cong\angle A$

• $\angle C\cong\angle Z$

• $\angle B\cong\angle Z$

• $\angle A\cong\angle Y$

Fill in the Blanks

The triangles are congruent by SSS postulate. Finish the congruence statement:

 $\Delta DOG\cong\Delta_{ }$ 

 

Multiple Select

After proving the triangles are congruent by HL Theorem, which statements are true for CPCTC?

• $\angle X\cong\angle V$

• $\angle U\cong\angle X$

• $XW\cong VW$

• $\angle XUW\cong\angle UWV$

Multiple Select

After proving the triangles are congruent by SAS postulate, which statements are true for CPCTC?

•  $\angle D\cong\angle A$  

•  $\angle B\cong\angle D$  
  

•  $DE\cong AE$  
  

•  $EC\cong AB$  

•  $BA\cong DC$