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Section 4.3 & 4.4: Proving s are Congruent - PowerPoint PPT Presentation

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

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

Q

N

R

P

S

Side-Side-Side (SSS)  Postulate

• If

If

Then

Then we can say:

Reasons

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

Reasons

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

X

P

W

S

Y

Side-Angle-Side (SAS)  Postulate

• If

If

)

)

Then

Then we can say:

Reasons

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

Reasons

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

Q

M

)

R

N

S

P

)

)

Angle-Side-Angle (ASA)  Postulate

• If

If

Then

Then we can say:

Reasons

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

3

4

2

Statements

Reasons

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

X

)

)

P

W

S

Y

)

)

Angle-Angle-Side (AAS)  Theorem

• If

If

Then

Then we can say:

Reasons

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

Reasons

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

40

40

50

50

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

(

A

D

F

(

C

B

Why Side-Side-Angle (SSA)Doesn’t Work

Theorem 4.8: Hypotenuse-Leg (HL)  Theorem

• If

D

A

If

Then

B

C

E

F

Then we can say:

Reasons

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