Transcript Lesson 4-2&4-3: Congruent Triangles

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 by SSS (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
1.
In ∆VGB, which sides include  B?
2. In ∆STN, which angle is included between
NS and TN ?
3. Which triangles can you prove congruent? Tell
whether you would use the SSS or SAS Postulate.
Y
A
P
X
B
4. What other information do you need to prove ∆DWO

∆DWG?
D
O
G
W
5. Can you prove ∆ SED
Explain.

∆BUT from the information given?
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
NEW ONES!
– AAS : a side after 2 angles
• What are the letter combinations we can’t
use?
AAA
A$$
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
1. Which side is included between  R and  F in ∆FTR?
2. Which angles in ∆ STU include US ?
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.
Q
H
3.
G
P
I
R
P
L
4.
Y
A
A
5.
B
X
C
Quiz
Tomorrow!
4-1, 4-2
4-3