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

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Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, &amp; 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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Presentation Transcript
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
• 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
• If 3 sides are congruent to other 3 sides

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

Rule

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
• 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
• 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

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
• 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!

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

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