Transcript 4.4 - MrsSicasMathWiki

4.4
ASA & AAS Congruence
HMWK:
p. 223, #s 8-18 All, 19-24, 29, 30
Game Plan: Today I will be able to
1. Prove s  using ASA and AAS
2. Apply  s to real world problems
3. Use constructions to copy s
Warm-up: If SSS represents side-side-side  and
SAS represents side-angle-side , describe the
meaning of the following.
1. AAA
2. AAS
3. SSA
4. ASA
4.4
ASA & AAS Congruence
Triangle Congruence
Angle Side Angle (ASA) Congruence Postulate: If
two angles and the included side of a triangle are
congruent to two angles and the included side of
another triangle, then the triangles are
congruent.
1. Sketch a diagram of this postulate.
2. Think – Pair – Share … explain
why this postulate is true.
4.4
ASA & AAS Congruence
Triangle Congruence
Angle Angle Side (AAS) Congruence Theorem: If two
angles and the nonincluded side of a triangle are
congruent to two angles and the nonincluded side of
another triangle, then the triangles are congruent.
1. Sketch a diagram of this postulate.
2. Think – Pair – Share … explain why this postulate is true. Be sure
to explain why we must have at least one pair of sides congruent.
4.4
ASA & AAS Congruence
Proving Congruent
Ex 1:
Is it possible to prove the following triangles
congruent?
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ASA & AAS Congruence
Proving Congruent
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ASA & AAS Congruence
Applying Congruent Triangles
Ex 3:
When searching for a missing airplane,
searchers used observations from people in
two different areas of a city. As shown, the
observers were able to describe sight lines A
from observers in different houses. One
sightline was from observers in House A and
the other sightline was fro observers in
House B. Assuming the sightlines are
accurate, did the searchers have enough
information to locate the airplane?


B

C
Hint: Think about what information we know about the triangle …angles? sides?
4.4
ASA & AAS Congruence
Copying a Triangle
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Need construction tools
Draw a triangle (relatively large).
Label the triangle ABC
Draw a line and label the line m
Follow along together.
Draw another triangle and switch with a
partner to copy.
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ASA & AAS Congruence
Wrap -up
What information do you need to know in order to
apply the 1) ASA postulate, and 2) AAS
theorem?
Tomorrow …
1. More on proving triangles congruent
2. Looking at a quiz on Wednesday or Thursday …
a proof quiz.
3. Remember projects are due on Wednesday!!!