Lesson 4 2 triangle congruence sss sas asa aas
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Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS PowerPoint PPT Presentation


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Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS. Vocab SSS (side-side-side) congruence Included angle SAS (side-angle-side) congruence. Draw the following figures using a ruler. Draw a triangle, measure its lengths

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Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS

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Lesson 4 2 triangle congruence sss sas asa aas

Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS

Vocab

SSS (side-side-side) congruence

Included angle

SAS (side-angle-side) congruence


Draw the following figures using a ruler

Draw the following figures using a ruler

  • Draw a triangle, measure its lengths

  • Draw another triangle in a different “manner” using the same length sides.

  • Are the 2 triangles different? Are they the same shape, same size?

They’re

Congruent!


Sss congruence

SSS congruence

  • If 3 sides are congruent to other 3 sides

    → ∆’s congruent bySSS (side-side-side)

    Rule


Draw the following figures using a ruler1

Draw the following figures using a ruler

  • A triangle with a 900 angle. Measure only the 2 sides that touch the 900

  • Draw another triangle in a different “manner” using the 2 measured lengths and 900 angle between them

  • Are the 2 triangles different? Are they the same shape, same size?

They’re

Congruent!


Sas congruence

SAS congruence

  • If 2 sides and the included angle between them are congruent to other 2 sides and the included angle

    → ∆’s congruent by SAS (side-angle

    side) Rule

    → Look for SAS – list S or A in order

8

8

750

750

12

12


Examples

Examples

  • In ∆VGB, which sides include B?

    2. In ∆STN, which angle is included between

    and ?

    3. Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate.

Y

A

P

X

B


Lesson 4 2 triangle congruence sss sas asa aas

D

4. What other information do you need to prove ∆DWO∆DWG?

5. Can you prove ∆SED ∆BUT from the information given? Explain.

O

G

W

U

T

D

E

S

B


Proving congruence in s

Proving Congruence in ∆’s

  • Go in a circle around triangle naming markings or measures in order (S or A)

  • ∆’s congruent if :

    • SSS : all 3 sides

    • SAS : an angle between (included) 2 sides

    • ASA : a side between 2 angles

    • AAS : a side after 2 angles

NEW ONES!


Lesson 4 2 triangle congruence sss sas asa aas

  • What are the letter combinations we can’t use?

AAA

A$$


Hints

Hints

  • Use facts/rules to find any missing angle or side measures first

    • Is a side congruent to itself?

    • Can you use any angle facts to find missing angle measures?

    • Look for parallel lines


Lesson 4 2 triangle congruence sss sas asa aas

  • Which side is included between R and F in∆FTR?

  • 2. Which angles in ∆ STU include ?

  • Tell whether you can prove the triangles congruent by ASA or

  • AAS. If you can, state a triangle congruence and the postulate

  • or theorem you used. If not, write not possible.

  • 3.

  • 4.

  • 5.

Q

H

G

P

I

R

P

L

Quiz

Tomorrow!

4-1, 4-2

4-3

Y

A

A

B

C

X


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