Section 4 3 4 4 proving s are congruent
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Section 4.3 & 4.4: Proving s are Congruent. Goals. Identify  figures and corresponding parts Prove that 2  are . Anchors. Identify and/or use properties of congruent and similar polygons Identify and/or use properties of triangles. M. Q. N. R. P. S.

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Section 4 3 4 4 proving s are congruent

Section 4.3 & 4.4: Proving s are Congruent

Goals

  • Identify  figures and corresponding parts

  • Prove that 2  are 

Anchors

  • Identify and/or use properties of congruent and similar polygons

  • Identify and/or use properties of triangles


Side side side sss postulate

M

Q

N

R

P

S

Side-Side-Side (SSS)  Postulate

  • If

If

Then

Then we can say:


Given w is the midpoint of qs pq ts and pw tw prove pqw tsw

Statements

Reasons

Given: W is the midpoint of QS PQ  TS and PW  TWProve: PQW  TSW


Given d is the midpoint of ac abc is isosceles prove abd cbd

Statements

Reasons

Given: D is the midpoint of ACABC is isoscelesProve: ABD  CBD


Side angle side sas postulate

Q

X

P

W

S

Y

Side-Angle-Side (SAS)  Postulate

  • If

If

)

)

Then

Then we can say:


Given qrs is isosceles rt bisects qrs prove qrt srt

Statements

Reasons

Given: QRS is isosceles RT bisects QRSProve: QRT  SRT


Given bd and ae bisect each other prove abc edc

Statements

Reasons

Given: BD and AE bisect each otherProve: ABC  EDC


Angle side angle asa postulate

)

Q

M

)

R

N

S

P

)

)

Angle-Side-Angle (ASA)  Postulate

  • If

If

Then

Then we can say:


Given b n rw bisects bn prove bro nwo

Statements

Reasons

Given: B  N RW bisects BNProve: BRO  NWO


Given 1 2 cd bisects bce prove bcd ecd

1

3

4

2

Statements

Reasons

Given: 1  2 CD bisects BCEProve: BCD  ECD


Angle angle side aas theorem

Q

X

)

)

P

W

S

Y

)

)

Angle-Angle-Side (AAS)  Theorem

  • If

If

Then

Then we can say:


Given ad ec b is the mdpt of cd prove abd ebc

Statements

Reasons

Given: AD ║ EC , B is the mdpt of CDProve: ABD  EBC


Given ad ec b is the mdpt of cd prove abd ebc1

Statements

Reasons

Given: AD ║ EC , B is the mdpt of CDProve: ABD  EBC


Why angle angle angle aaa doesn t work

40

40

50

50

Why Angle-Angle-Angle (AAA)Doesn’t Work


Why side side angle ssa doesn t work

E

(

A

D

F

(

C

B

Why Side-Side-Angle (SSA)Doesn’t Work


Theorem 4 8 hypotenuse leg hl theorem
Theorem 4.8: Hypotenuse-Leg (HL)  Theorem

  • If

D

A

If

Then

B

C

E

F

Then we can say:


Given rs qt qrt is isosceles prove qrs trs

Statements

Reasons

Given: RS  QT QRT is isoscelesProve: QRS  TRS


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