Name ________________________________________ Date __________________ Class__________________
LESSON
2-5
Reading Strategies
Building Vocabulary
When you look into a mirror, you see your reflect ion. You see your exact,
identical self. Similarly, when you use the Reflexive Property of Equality,
a quantity is equal to its exact, identical self.
5=5
2 x + 3 = 2x + 3
m∠C = m∠C
The two halves of a football field are symmetrical to each other. When two
football teams change sides, the second side of the field is the same as the
first side. In the same way, the Symmetric Property of Equality allows
equal quantities to be written on either side of the equal sign.
If x = 2, then 2 = x.
If m∠A = 40°, then 40° = m∠A.
Just as the cars on a train link the engine to the caboose, the Transitive
Property of Equality links equal quantities to each other. If two
expressions are equal to the same thing, they are equal to each other.
If AB = 8 and 8 = CD,
then AB = CD.
AB = CD
Sometimes, at school, a substitute teacher may replace your teacher for a
day. Similarly, the Substitution Property of Equality allows equal
expressions to be used interchangeably.
If b = 5 and a + b = 9, then a + 5 = 9.
Which properties do the following situations describe?
1. butterfly wings
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2. removing the quarterback of the football team
and replacing him with another quarterback
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3. the reflection of clouds on a still pond
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4. There are four quarters in one dollar and ten
dimes in one dollar, so four quarters have the
same value as ten dimes.
_________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-42
Holt McDougal Geometry
Reading Strategies
Statements
1. Symmetric Property of Equality
Reasons
2. Substitution Property of Equality
1. a. ∠HKJ is a straight
angle.
1. Given
3. Reflexive Property of Equality
2. m∠HKJ = 180°
2. b. Def. of straright ∠
4. Transitive Property of Equality
JJG
3. c. KI bisects ∠HKJ
3. Given
4. ∠IKJ ≅ ∠IKH
4. Def. of ∠ bisector
5. m∠IKJ = m∠IKH
5. Def. of ≅
6. d. m∠IKJ + m∠IKH =
m∠HKJ
6. ∠ Add. Post.
7. 2m∠IKJ = 180°
7. e. Subst. (Steps 2, 5, 6)
8. m∠IKJ = 90°
8. Div. Prop. of =
9. ∠IKJ is a right angle.
9. f. Def. of right ∠
2-6 GEOMETRIC PROOF
Practice A
1. B
2. A
3. B
4. C
5. two-column
6.
Statements
1. a. ∠1 and ∠2 are
straight angles.
Reasons
Practice C
1. Given
1.
2. m∠1 = 180°, m∠2 = 180° 2. b. Def. of straight ∠
3. m∠1 = m∠2
3. Subst. Prop. of =
4. c. ∠1 ≅ ∠2
4. Def. of ≅ ∠s
Statements
7.
Statements
Reasons
1. ∠1 and ∠2 form a linear pair,
and ∠3 and ∠4 form a linear
pair.
2. ∠1 and ∠2 are
supplementary, and ∠3 and
∠4 are supplementary.
1. a. Given
Reasons
1. m∠2 + m∠3 + m∠4 =
180°
1. Given
2. ∠1 and ∠2 are
supplementary.
2. Linear Pair
Thm.
3. m∠1 + m∠2 = 180°
3. Def. of supp. ∠s
4. m∠1 + m∠2 = m∠2 +
m∠3  m∠4
4. Subst. Prop. of
=
5. m∠1 = m∠3 + m∠4
5. Subtr. Prop. of
=
2. b. Linear Pair
Thm.
3. c. m∠1 + m∠2 = 180°, and
m∠3 + m∠4 = 180°
3. Def. of supp.
4. m∠1 + m∠2 + m∠3 + m∠4 =
360°
4. d. Add. Prop.
of =
2. Possible answer:
Statements
∠s
Practice B
1. Given
∠s
2. Def. of mdpt.
3. Def. of ≅ segments
Reasons
1. ∠1 is a right angle.
1. Given
2. ∠1 and ∠2, ∠1 and ∠4, ∠2
and ∠3 are supplementary.
2. Linear Pair
Thm.
3. ∠1 ≅ ∠3
3. Congruent
Supps. Thm.
4. ∠3 is a right angle.
4. Rt. ∠ ≅ Thm.
5. Def. of supp. ∠s
4. Seg. Add. Post.
5. Subst.
5. m∠1 + m∠2 = 180°,
m∠1 + m∠4 = 180°
6. Given
7. Mult. Prop. of =
6. m∠1 = 90°
6. Def. of rt. ∠
7. 90° + m∠2 = 180°,
90° + m∠4 = 180°
7. Subst.
8. m∠2 = 90°, m∠4 = 90°
8. Subtr. Prop. of =
9. ∠2 and ∠4 are right angles.
9. Def. of rt. ∠
8. Subst. Prop. of =
9. Def. of ≅ segments
10.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A17
Holt McDougal Geometry