Download ASA, AAS

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LESSON
5-2
Practice A
Triangle Congruence: ASA, AAS, and HL
Name the included side for each pair of
consecutive angles.
1. ‘X and ‘Z ________
2. ‘Y and ‘X ________
3. ‘Y and ‘Z ________
Write ASA (Angle-Side-Angle Congruence), AAS (Angle-Angle-Side Congruence),
or HL (Hypotenuse-Leg Congruence) next to the correct postulate.
4. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse
and a leg of another right triangle, then the triangles are congruent.
_________
5. If two angles and a nonincluded side of one triangle are congruent to the
corresponding angles and nonincluded side of another triangle, then the
triangles are congruent.
_________
6. If two angles and the included side of one triangle are congruent to two angles
and the included side of another triangle, then the triangles are congruent.
_________
For Exercises 7–9, tell whether you can use each congruence
theorem to prove that UABC > UDEF. If not, tell what else
you need to know.
7. Hypotenuse-Leg
_________________________________________________________________________________________
8. Angle-Side-Angle
_________________________________________________________________________________________
9. Angle-Angle-Side
_________________________________________________________________________________________
1
10. A standard letter-sized envelope is a 9 -in.-by-4-in.
2
rectangle. The envelope is folded
and glued from a sheet of paper shaped
like the figure. Use the phrases in the
word bank to complete this proof.
Given: JMNK is a rectangle. ‘IJK > ‘LMN, ‘IKJ > ‘LNM
Prove: UIJK > ULMN
Statements
Given,
ASA,
Definition of rectangle
Reasons
1. ‘IJK > ‘LMN, ‘IKJ > ‘LNM
1. a. ______________________________
2. JK # MN
2. b. ______________________________
3. UIJK > ULMN
3. c. ______________________________
© Houghton Mifflin Harcourt Publishing Company
129
Holt McDougal Analytic Geometry
4. Postulates are accepted as being true
without proof, while a theorem has been
proven.
2.
Statements
Reasons
1. LK # HJ ,GK # GJ
1. Given
5. SSS
6. SAS
2. LK
HJ, GK
2. Def. of #
7. neither
8. SAS
3. KJ
KJ
GJ
segments
4. LK KJ
HJ KJ
3. Reflex. Prop. of
5. LK KJ
LJ,
4. Add. Prop. of
HJ KJ
HK
5. Seg. Add. Post.
6. LJ HK
7. LJ # HK
8. ‘GKL # ‘GJH
9. ‘GKL and ‘GKJ are
5-2 TRIANGLE CONGRUENCE: ASA,
AAS, AND HL
Practice A
6. Subst.
7. Def. of #
segments
8. Given
1. XZ
2. YX
3. YZ
4. HL
5. AAS
6. ASA
supplementary;
9. Linear Pair Thm.
7. No; you need to know that AC # DF .
‘GJH and ‘GJK
10. Congruent
8. Yes, if you use Third ‘s Thm. first.
are supplementary.
Supplements Thm.
9. Yes
10. ‘GKJ # ‘GJK
11. SAS (Steps
11. UGLJ # UGHK
1, 7, 10)
10.
Statements
1. ‘IJK # ‘LMN, ‘IKJ
# ‘LNM
Problem Solving
1. We know that AB # DC . ‘ADC and
‘DAB are right angles, so ‘ADC # ‘DAB
by Rt. ‘ # Thm. AD # DA by Reflex.
Prop. of #. So UABD # UDCA by SAS.
1. a. Given
2. JK # MN
2. b. Definition of
rectangle
3. UIJK # ULMN
3. c. ASA
Practice B
2. We know that AK # BK . Since J is the
1. No; you need to know that AB # CB.
midpoint of AB, AJ # BJ by def. of
2.
3.
4.
6.
8.
midpoint. JK # JK by Reflex. Prop. of #.
So UAKJ # UBKJ by SSS.
3. By the U Sum Thm., m‘H 54°. For x
6, WY FH 10 in., m‘Y m‘H 54°,
and XY HG 12 in. So UWXY # UFHG
by SAS.
4. A
Reasons
5. G
Reading Strategies
1. Both involve the sides of the two triangles
being compared.
2. Postulate SAS involves comparing
included angles within the triangles, while
SSS compares only the sides.
3. Postulates and theorems are both
statements that can be used to compare
geometric shapes.
Yes
Yes, if you use Third ‘s Thm. first.
5. ASA or AAS
HL
7. AAS or ASA
none
Possible answer: All right angles are
congruent, so ‘QUR # ‘SUR. ‘RQU
and ‘PQU are supplementary and ‘RSU
and ‘TSU are supplementary by the
Linear Pair Theorem. But it is given that
‘PQU # ‘TSU, so by the Congruent
Supplements Theorem, ‘RQU # ‘RSU.
RU # RU by the Reflexive Property of #,
so URUQ # URUS by AAS.
© Houghton Mifflin Harcourt Publishing Company
A26
Holt McDougal Analytic Geometry