Geometric Proofs of Congruent Triangles

Triangle proofs

By: Jacob Preis

Here is a reference sheet. make sure to take a picture of it!

Poll

Warm-up: What word appropriately goes into the box. (don't worry this is a poll so you won't be marked as wrong!)

• definition of midpoint

• SAS

• Given

• vertical angles are congruent

basic triangle proofs

• should be easy!

• Helps you know why the triangles are congruent.

• you can do the same thing with transversals(we are not doing that yet)

Poll

what do you think about triangle proofs so far?

• AWESOME!😎😎😎😎🐈🐈😉

• good.😐😐😐

• NOT GOOD AT ALL.😠😠😠😠😩😩😤

Multiple Choice

Identify the missing statement or reason. (this is just for practice to see if you remember this.)

• Reflexive Property

• Definition of Midpoint

• Given

• Vertical Angles Theorem

Open Ended

what do you recognize about reflexive property? (perhaps when we did reflections across the axis...)

Here are some examples od Statements there are!

here of some examples for the reasons

• Vertical Angles are congruent

• definition of bisector

• definition of perpendicular bisector

• definition of midpoint

Poll

Do you think you got this?

• YES😎😎

• NO😕😕😤

Part 2: practice quiz

By: Jacob Preis

Open Ended

Practice Q1: Given:

$$\overline{LN}\ \cong\overline{NP}$$  and  $$\overline{MN}\ \cong\overline{NO}$$  
Prove:  $$\Delta LNM\cong\Delta PNO$$  

Open Ended

Practice Q2: Given:

$$\overline{IF}\ \cong\overline{HG}$$  and  $$\overline{FG}\ \cong\overline{IH}$$  
Prove:
$$\Delta IFG\cong\Delta GHI$$  

Open Ended

Practice Q3: Given:

$$\overline{ST}\ \cong\overline{UP}$$  and  $$\angle STU\ \cong\angle TUP$$  
Prove: 
$$\Delta STU\ \cong\Delta PUT$$  

Open Ended

practice Q4: Given:

$$\overline{TU}\ \cong\overline{UV}$$  and M is the midpoint of  $$\overline{VT}$$  
Prove:
$$\Delta TUM\cong\Delta VUM$$  

Poll

How well do you think you have done on a scale from 1 - 5?

• 1

• 2

• 3

• 4

• 5

Part 3: Graded quiz

By: Jacob Preis

Fill in the Blank

Q1: fill in the blank:

(hint: it either SSS, SAS, or ASA)

Open Ended

Q2: Given:

$$\overline{TS}\ \cong\overline{QR}$$  and  $$\overline{RS}\cong\overline{QT}$$  
Prove:
$$\Delta QRS\ \cong\Delta SRQ$$  

Open Ended

Q3: Given:

Point S is midpoint of  $$\overline{HI}\ and\ \overline{LT}$$  
Prove:
$$\Delta LSH\cong\Delta IST$$  
(Hint: Draw it on a piece of paper!!!)

Open Ended

Q4: Given:

$$\overline{AD}\cong\overline{BC}$$  and  $$\angle BDA\cong\angle BDC$$  
Prove:

$$\Delta ABD\cong\Delta BDC$$  
(hint: REMEMBER TO DRAW IT ON A PIECE OF PAPER SENSE THERE IS NO PICTURE)

Open Ended

Q5: Given:


$$\angle WXS\cong\angle YXS$$  and  $$\angle WSX\cong\angle YSX$$  

Prove: 

$$\Delta WXS\cong\Delta YXS$$  
(hint: don't forget to draw it out sense there is not a picture.)

END OF QUIZ

Poll

How do you feel about all this?

• AWESOME!!!👍👍😎😎🐱🐱

• good.😐😐

• THE WORST.😩😩😩😠😠

The End!

Thanks for completing this!