Download LESSON 4-3 NOTES: TRIANGLE CONGRUENCE BY ASA AND

LESSON 4-3 NOTES:
TRIANGLE CONGRUENCE BY ASA AND AAS
In this lesson, you will prove triangles congruent by using one pair of corresponding sides and two
pairs of corresponding angles. Remember that an included side is a side "between" two angles of
a triangle and that an included angle is an angle "between" two sides of a triangle.
Postulate 4-3: Angle-Side-Angle (ASA) Postulate
If two angles and the included side of one
triangle are congruent to two angles and
the included side of another triangle, then
the two triangles are congruent.
If ∠A ∠D,
then ∆ABC ∆DEF
and ∠C
B
∠F,
E
A
C
D
F
Examples: Which two triangles are congruent by ASA? Write a congruence statement.
1.
2.
Proof: Complete the following proof.
Given:
3.
C
D
,
∠B and ∠E are right angles.
Prove: ∆ABC
∆AED
A
E
B
STATEMENTS
1)
2)
REASONS
1)
∠B and ∠E are right angles
2)
3)
3)
4)
4)
5)
5)
Theorem 4-2: Angle-Angle-Side (AAS) Theorem
If two angles and a nonincluded side of one
triangle are congruent to two angles and the
corresponding nonincluded side of another
triangle, then the two triangles are congruent.
If ∠A ∠D, ∠B ∠E and
then ∆ABC ∆DEF.
B
,
E
A
C
D
F
The AAS Theorem can be proved using the ASA Postulate. In ∆ABC and ∆DEF above, we know
that ∠C ∠F. Why? Because we know ∠C ∠F, can we now use the ASA Postulate to prove
∆ABC ∆DEF?
M
R
Proof: Complete the following proof.
Given:
∠M
∠K,
Prove:
∆WMR
||
∆RKW
K
W
STATEMENTS
REASONS
1)
1)
2)
2)
3)
3)
4)
4)
5)
5)
What additional information would you need to prove each pair of triangles congruent by
the stated postulate or theorem?
4. ASA Postulate
7. AAS Theorem
5. AAS Theorem
8. AAS Theorem
6. ASA Postulate
9. ASA Postulate