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LESSON
5-6
Reading Strategies
Identify Relationships
Keep two ideas in mind when considering the angles and sides of a triangle.
If two sides of one triangle are congruent to
two sides of another triangle and the
included angles are not congruent, then the
longer third side is across from the larger
included angle.
If two sides of one triangle are congruent to
two sides of another triangle and the third
sides are not congruent, then the larger
included angle is across from the longer
third side.
In these triangles, m∠Q > m∠T, which
means that RS > UV.
In these triangles, AB > GH, which means
that m∠C > m∠F.
Use the relationships above to compare the following measurements.
1.
2.
Compare m∠ADB and m∠DBC.
Compare ZY and WZ.
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4.
3.
Compare m∠ABC and m∠EFD.
Compare QR and RS.
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-50
Holt McDougal Geometry
9. The segments can form a triangle.
Challenge
1. AB ≅ AD and AC ≅ AE because radii of
the same circles are congruent. Since
m∠BAC > m∠DAE, then by the Hinge
Thm., BC > DE.
2. 16.5 < y < 34
10. 11
11. 130; 121
12. acute
Practice B
1.
3. 0.25 < z < 3
2. 2 14
61
3. 48
4.
Statements
Reasons
1. JK || HL , JK ≅ HL ,
m∠KML > m∠HML
1. Given
2. ∠JMK ≅ ∠LMH
2. Vert. ∠s Thm.
3. ∠JKH ≅ ∠LHK
3. Alt. Int. ∠s Thm.
4. UJKM ≅ ULHM
4. AAS
5. MK ≅ MH
5. CPCTC
6. ML ≅ ML
6. Reflex. Prop. of ≅
7. KL > HL
7. Hinge Thm.
Problem Solving
1. Greatest at relaxed position; least at
writing position; the length of his leg and
the length of his body are the same in all
three triangles. So, by the Converse of
the Hinge Thm., the larger included ∠ is
across from the longer third side.
4. height: 25.2 in.; width: 33.6 in.
6. 2.5; no
7. 25; yes
8. 3 10; no
9. yes; acute
10. yes; obtuse
11. yes; obtuse
12. Possible answer: The triangle is obtuse,
so Kitty is correct. But Kitty did not use
the Pythagorean Inequalities Theorem
correctly. The measure of the longest
side should be substituted for c, so 169 +
64 < 256 is the inequality that shows that
the triangle is obtuse.
Practice C
1. Possible answer: When using the
Pythagorean Inequalities Theorem, the
longest side of the triangle is substituted
for c, and the angle opposite that side is
determined as right, acute, or obtuse. The
longest side in a triangle is opposite the
largest angle. So if the angle opposite the
longest side is acute, then the other two
angles must also be acute.
2. the second cyclist
3. The ∠ formed by the compass when
drawing the first circle is smaller. So the
distance between the points of the
compass is greater for the second circle.
4. B
5. 51.4 in.
2.
5. G
13; − 13
3. Possible answer: Segments must have
positive lengths. A negative length does
not make sense. In geometry, only
positive square roots are used.
Reading Strategies
1. m∠ADB < m∠DBC
2. ZY > WZ
3. m∠ABC < m∠EFD
4. QR < RS
5-7 THE PYTHAGOREAN THEOREM
2. 16
3. 8.9
4. 48 in.
5. whole numbers
6. 7.2; no
7. 11.5; no
8. 12; yes
5.
6. 18 65
7. 5000
8.
Practice A
1. 26
4. no; 0.128
34; 3 34
41
2
Reteach
1. x = 12
2. x =
3. x =
4. x = 40
39
29
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A56
Holt McDougal Geometry