Download Triangle Congruence by ASA and AAS

4-3
PART 1
Triangle Congruence
by ASA and AAS
Vocabulary
1. Cross out the figure(s) that are NOT triangle(s).
2. A triangle is a polygon with
sides.
3. A triangle with a right angle is called a(n)
obtuse / right / scalene triangle.
Vocabulary Builder
corresponding sides
A
X
Other Word Forms: correspond (verb),
correspondence (noun)
Definition: Corresponding means similar in position,
purpose, or form.
C Y
B
Z
Math Usage: Congruent figures have congruent
corresponding parts.
Use Your Vocabulary
Draw a line from each part of kABC in Column A to the corresponding part of
kXYZ in Column B.
Column A
Column B
4. BC
/Z
5. /A
/Y
6. AB
YZ
7. /C
/X
8. AC
XY
9. /B
XZ
Chapter 4
206
B
A
Y
C
Z
X
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corresponding (adjective) kawr uh SPAHN ding
Postulate 4–3 Angle-Side-Angle (ASA) Postulate
Postulate
If . . .
Then . . .
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.
/A > /D, AC > DF, /C > /F
nABC > nDEF
B
A
E
C
D
F
10. Explain how the ASA Postulate is different from the SAS Postulate.
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Problem 1 Using ASA
Got It? Which two triangles are congruent by ASA? Explain.
H
C
F
O
N
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
G
A
I
T
11. Name the triangles. List the vertices in corresponding order: list the vertex with the
one arc first, the vertex with the two arcs second, and the third vertex last.
12. /G > /
>/
13. /H > /
>/
14. HG >
>
15. The congruent sides that are included between congruent angles are
and
.
16. Write a congruence statement. Justify your reasoning.
n
> n
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207
Lesson 4-3, Part 1
Problem 2
Writing a Proof Using ASA
Got It? Given: lCAB O lDAE, BA O EA, lB and lE are right angles
C
D
Prove: kABC O kAED
A
B
17. Circle the information that you are given.
Two angles and the included side of one
triangle are congruent to two angles and
the included side of another triangle.
E
Two sides and the included angle of one
triangle are conguent to two sides and
the included angle of another triangle.
18. Complete the flow chart to prove nABC > nAED.
Given
/B and /
are right angles.
Given
Given
BA ˘
/CAB ˘ /
All right angles are congruent.
ASA Postulate
nABC ˘
/B ˘
Lesson Check • Do you UNDERSTAND?
Error Analysis Your friend asks you for help on a geometry exercise. Below is your
friend’s paper. What error did your friend make? Explain.
∆LMN ∆QRS
by ASA.
R
L
N
Q
19. Circle the side in nLMN that is included between /L and /N.
LM
LN
MN
20. Circle the side in nQRS that is included between side of /Q and /S.
QR
QS
RS
21. Do you know whether the included sides you circled in
Exercises 19 and 20 are congruent?
Yes / No
22. What error did your friend make? Explain.
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Chapter 4
208
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
S
M