Download Practice B

Name ________________________________________ Date __________________ Class__________________
LESSON
4-5
Practice B
Triangle Congruence: ASA, AAS, and HL
Students in Mrs. Marquez’s class are watching a film on the uses of geometry
in architecture. The film projector casts the image on a flat screen as shown in
the figure. The dotted line is the bisector of ∠ABC. Tell whether you can use
each congruence theorem to prove that UABD ≅ UCBD. If not, tell what else you
need to know.
1. Hypotenuse-Leg
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2. Angle-Side-Angle
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3. Angle-Angle-Side
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Write which postulate, if any, can be used to prove the pair of
triangles congruent.
4. ______________________
5. ______________________
6. ______________________
7. ______________________
Write a paragraph proof.
8. Given: ∠PQU ≅ ∠TSU,
∠QUR and ∠SUR are right angles.
Prove: URUQ ≅ URUS
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4-36
Holt Geometry
have enough information to draw the
triangle; if the three parts are the three
angles.
statements that can be used to compare
geometric shapes.
4. Postulates are accepted as being true
without proof, while a theorem has been
proven.
5. SSS
6. SAS
7. neither
8. SAS
2. In right triangles, one of the three angles
is known, and all right angles are
congruent. This means that fewer parts
must be shown congruent to prove two
right triangles congruent. LL is a special
case of SAS in which the A is the right
angle. HA is a special case of AAS in
which the first A is the right angle. LA is a
special case of ASA in which one A is a
right angle.
LESSON 4-5
Practice A
1. XZ
2. YX
3. YZ
4. HL
5. AAS
6. ASA
3. Yes; possible answer: If the two parts
given are both angles, then the angle
measures are set, but the side lengths
are not.
7. No; you need to know that AC ≅ DF .
8. Yes, if you use Third ∠s Thm. first.
4. Possible answer: GB, GD and GF all
have the same length, by the definition of
the radius of a circle, and so they are all
congruent. Each radius is perpendicular
to its side of the triangle, so all those
angles are right angles, and they are all
congruent. GE is congruent to GE by
the Reflexive Property, and thus the
conditions for HL congruence between
UFGE and UDGE have been met.
Similar reasoning shows that UFGA is
congruent to UBGA and that UBGC is
congruent to UDGC. ∠EGD and ∠AGB
are vertical angles, so they are
congruent. This fact, and the
congruencies already shown, meet the
conditions for ASA congruence between
UEGD and UBGA. Similar reasoning
shows that UFGE is congruent to UBGC
and UFGA is congruent to UDGC. The
Transitive Property of Congruence can
now be used to show that all the triangles
within UACE are congruent. When
triangles have been proven congruent, it
is known that each matching part of the
triangles is congruent. Hence AB = BC =
CD = DE = EF = FA. By the Addition
Property of Equality and the Segment
Addition Postulate, AC = CE = EA and
thus UACE is equilateral.
9. Yes
10.
Statements
1. ∠IJK ≅ ∠LMN, ∠IKJ
≅ ∠LNM
Reasons
1. a. Given
2. JK ≅ MN
2. b. Definition of
rectangle
3. UIJK ≅ ULMN
3. c. ASA
Practice B
1. No; you need to know that AB ≅ CB.
2. Yes
3. Yes, if you use Third ∠s Thm. first.
4. HL
5. ASA or AAS
6. none
7. AAS or ASA
8. 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.
Practice C
1. angle, one adjacent side, and the side
opposite the angle, then you might not
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt Geometry