Unit 5 Congruent and Similar Triangles Review

Go watch this video.

TAKE NOTES.

You need to know rotation, translation, and reflection.

https://www.youtube.com/watch?v=m73VMHLzt-4

Take notes.

Take notes.

Multiple Choice

A turn is also called a ___________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

A slide is also called a _________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

• B' (2 , 4.5)

• B' (-8 ,-18)

• B' (8 ,18)

• B' (9 ,4)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Reflections over the y-axis

(x,y) -> (-x,y)

Multiple Choice

What are the coordinates for C' after a reflection over the y-axis?

• (1,2)

• (-1,-2)

• (2,1)

• (-1,2)

Rotation

• turning shapes about the origin

Multiple Choice

Triangle EFG will be rotated 90 degrees counterclockwise about the origin. What will be the coordinates of E'?

• (-2,-1)

• (-1,-2)

• (1,-2)

• (2,1)

Multiple Choice

Rotate the point (5,5) around the origin 180 degrees counterclockwise. State the image of the point.

Rule: (x, y) ---- ( -x, -y)

• (5,-5)

• (5,5)

• (-5,-5)

• (-5,5)

Multiple Choice

Rotate the point (7,8) around the origin 90 degrees counter clockwise. State the image of the point.

Rule: (x, y) ---- ( -y, x)

• (-7,-8)

• (8,-7)

• (-8,7)

• (8,7)

​Dilations

​non-rigid transformation that enlarges or shrinks a mathematical element using a specific scale factor

​changes the position and size of a figure, but not the shape.

​If k is a fraction then the image is shrinking and if k is a whole number the image is enlarging

Fill in the Blanks

Describe the dilation

Triage ABC is dilated by a factor of _ to make triangle A'B'C'

Fill in the Blanks

Describe the dilation

Rectangle GHIJ is dilated by a factor of _ to make rectangle G'H'I'J'

Congruent Triangles Review

Multiple Choice

True or False:

The order MATTERS when writing our congruency statements.

• True

• False

Multiple Choice

Find the $$m\angle1$$  

• $$125\degree$$  

• $$180\degree$$  

• $$90\degree$$  

• $$55\degree$$  

Multiple Choice

$$\Delta LMN\cong\Delta ZXY$$  

Find the  $$m\angle1$$  

• $$30\degree$$  

• $$40\degree$$  

• $$20\degree$$  

• $$180\degree$$  

Multiple Choice

Find the value of x.

• 115

• 81

• 65

• 55

4.1 - Congruent Triangles

​By Vinícius Weite Thomé - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49327560

​Objective:

​To recognize congruent triangles and their corresponding parts.

​New Term:

​Congruent Triangles:

​

​Triangles with the same size and shape are congruent.

​

​This means that all the corresponding parts (sides and angles) are congruent.

("Corresponding parts"? Put your fingertips together. Your corresponding fingers are touching. Thumb to thumb, ring finger to ring finger, so forth)

​Congruency statement

​CPCTC

​This works in the opposite direction as well. If we know two triangles are congruent, that means that all their pairs of corresponding parts are congruent. We use the abbreviation CPCTC:

​

​Corresponding Parts of Congruent Triangles are Congruent

Open Ended

Given the congruency statement $$\Delta JKL\cong\Delta PQR$$  list all pairs of congruent sides and angles on your fillable notes.

Multiple Choice

Given the congruency statement $$\Delta WXY\cong\Delta EFG$$  what is another valid congruency statement?

• $$\Delta YWX\cong\Delta GEF$$  

• $$\Delta XYW\cong\Delta FGE$$  

• $$\Delta WYX\cong\Delta EGF$$  

• All are valid congruency statements for this pair of triangles.

Multiple Choice

Which is a correct congruence statement.

• A
• B
• C
• D

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• AAS

Multiple Choice

∠A = ≅

• ∠M

• ∠N

• ∠L

8.1 Congruent Triangles Theorems

I can use triangle congruence theorems to solve problems.

Multiple Choice

Complete the congruence statement.

• CRP
• PCR
• RPC
• PRC

Multiple Choice

State if the two triangles are congruent.  If they are, state which theorem you would use.

• Yes, SAS
• Yes, SSS
• Yes, HL
• No

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SAS
• ASA
• SSS
• Not Possible

Multiple Choice

• Congruent by HL
• Congruent by SAS
• Congruent by SSS
• Not Necessarily Congruent

Multiple Choice

Are the triangles congruent, if yes, why?

• SSS
• SAS
• ASA
• Not Congruent

Multiple Choice

Are the triangles congruent, if yes, why?

• SSS
• ASA
• AAA
• Not Congruent

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SAS
• ASA
• AAS
• Not Possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SAS
• ASA
• AAS
• Not Possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• AAS
• Not Possible

Multiple Choice

∆EHG≅∆KFC
Which is a true statement?

• EH≅FK
• HG≅KF
• EG≅KC
• ∠E≅∠C

Multiple Choice

∆ABC≅∆XYZ
which is true?

• AB≅XY
• AB≅YZ
• AB≅XZ
• BC≅CB

Multiple Choice

What is the correct congruence statement? ΔDEC ≅________

• ΔAEB

• ΔEAB

• ΔBEA

• Not Congruent

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS

• SAS

• ASA

• Not Possible

Multiple Choice

Which of the following is not a valid reason to prove congruent triangles?

• SSA
• ASA
• SAS
• SSS

Multiple Choice

What does SSS stand for?

• Small Small Small

• Side Side Side

• Small Side Small

• Sam's Silly Side

Multiple Choice

What does CPCTC stand for?

• Congruent parts of congruent triangles are congruent
• Corresponding parts of congruent triangles are congruent
• Corresponding parts of corresponding triangles are corresponding
• Corresponding parts of congruent triangles are Canadian.

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 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 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 Choice

Are the following triangles similar?

• yes

• no

Multiple Choice

Are the following triangles similar?

• yes

• no

Multiple Choice

Are the following triangles similar?

• yes

• no

Multiple Choice

Are the following triangles similar?

• yes

• no

Multiple Choice

Are the following triangles similar?

• yes

• no

Multiple Choice

What is the included angle between sides LE and EG?

• L

• E

• G

Multiple Choice

Are the triangles below similar? If so, state the

postulate/theorem that justifies your answer.

• Yes, SSS

• Yes, SAS

• Yes, AA

• Not Similar

Multiple Choice

Are the triangles below similar? If so, state the

postulate/theorem that justifies your answer.

• Yes, SSS

• Yes, SAS

• Yes, AA

• Not Similar

Multiple Choice

Are the triangles below similar? If so, state the

postulate/theorem that justifies your answer.

• Yes, SSS

• Yes, SAS

• Yes, AA

• Not Similar

Multiple Choice

Are the triangles below similar? If so, state the

postulate/theorem that justifies your answer.

• Yes, SSS

• Yes, SAS

• Yes, AA

• Not Similar

Poll

Do you think these two triangles are similar?

• Yes

• No

Poll

Do you think these two triangles are similar?

• Yes

• No

Angle Angle Criterion

​For these two triangles, we can see..

• Angle P = Angle X

• If we solved for Angle R, it equals 50° (60+70=130, 180-30=150)

  • This is equal to Angle Z

• If we solved for Angle Y, it equals 70° (60+50=110, 180-110=70)

  • This is equal to Angle Q

This means that at least two angles from each triangle are equal, so the triangles are similar.

Multiple Choice

Are the triangles similar by angle-angle similarity?

• Yes
• No