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Lesson 4-1 Classifying Triangles
Lesson 4-2 Angles of Triangles
Lesson 4-3 Congruent Triangles
Lesson 4-4 Proving Congruence–SSS, SAS
Lesson 4-5 Proving Congruence–ASA, AAS
Lesson 4-6 Isosceles Triangles
Lesson 4-7 Triangles and Coordinate Proof
Example 2 Use AAS in Proofs
Example 3 Determine if Triangles Are Congruent
OBJECTIVE: To use AAS Theorem to test for triangle
congruence (2.9.8K) (M8.C.1.1)
THEOREM 4.5 – Angle-Angle-Side Congruence: If two
angles and a nonincluded side of one
triangle are congruent to the
corresponding two angles and side of a
second triangle, then the two triangles are
congruent.
Write a flow proof.
Given:
Prove:
Proof:
Write a flow proof.
Given:
Prove:
Proof:
STANCES When Ms. Gomez puts her hands on her hips,
she forms two triangles with
her upper body and arms.
Suppose her arm lengths AB
and DE measure 9 inches, and
AC and EF measure 11 inches.
Also suppose that you are
given that
Determine
whether ABC EDF.
Justify your answer.
Explore We are given measurements of two sides of
each triangle. We need to determine whether the
two triangles are congruent.
Plan
Since
Likewise,
We are given
Check each possibility using the five methods
you know.
Solve
We are given information about three sides. Since
all three pairs of corresponding sides of the
triangles are congruent, ABC EDF by SSS.
Examine You can measure each angle in ABC and EDF
to verify that
Answer: ABC EDF by SSS
The curtain decorating the window forms 2 triangles
at the top. B is the midpoint of AC.
inches and
inches. BE and BD each use the same amount
of material, 17 inches. Determine whether ABE CBD
Justify your answer.
Answer: ABE CBD by SSS
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