Ch 4.2 Triangle Congruence by SSS and SAS

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Transcript Ch 4.2 Triangle Congruence by SSS and SAS

4.2 Triangle Congruence by SSS &
SAS
Essential Question:
How do you prove triangles are congruent using the SSS and
SAS postulates?
• We know, if two triangles have three pairs of
congruent corresponding angles and three
pairs of congruent corresponding sides, then
the triangles are congruent.
• However, you do not need to know that all six
corresponding parts are congruent in order to
conclude that two triangles are congruent.
• You can use some of the corresponding parts
to deduce the same must be true for the rest
of the parts.
• Postulate 4-1
• Side-Side-Side (SSS) Postulate
– If the three sides of one triangle are congruent to
the three sides of another triangle, then the two
triangles are congruent.
– ΔGHF ≅ ΔPQR
P
G
Q
H
F
R
Example 1: Using SSS
Practice
• Given: HF ≅ HJ, FG ≅ JK. H is the midpoint of
GK.
F
J
• Prove: ΔFGH ≅ ΔJKH
G
H
K
• Postulate 4-2
• Side-Angle-Side (SAS) Postulate
– If the two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the two
triangles are congruent.
– ΔGHF ≅ ΔPQR
G
H
F
P
Q
R
Example 2: Using SAS
Practice
• What other information do you need to prove
A
ΔABC ≅ ΔCDA by SAS?
7
8
B
6
D
7
C
Practice
• What other information do you need to prove
ΔABC ≅ ΔCDA by SAS?
A
D
B
C
Example 3: Congruent?
Practice
Summary
• Answer the essential question in complete,
detailed sentences.
• How do you prove triangles are congruent
using the SSS and SAS postulates?
• Write 2-4 study questions in the left column
that correspond with the notes.