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LESSON
2-3
Reading Strategies
Graphic Organizer
Conjectures can be verified by using deductive reasoning.
Apply the Laws of Deductive Reasoning.
1.
If two angles are congruent, then they have the same measure. ∠BAC ≅ ∠CAD.
Conjecture: _______________________________________________________________
Hypothesis: _______________________________________________________________
The conjecture is (valid/invalid) _______________ using the Law of
_______________.
2.
You are given the following statements about ∠S:
If 90° < m∠S < 180°, then ∠S is obtuse. If ∠S is obtuse, then it is not a right angle.
Conjecture: _______________________________________________________________
If p → q and q → r, determine p, q, and r.
p: _______________________________________________________________________
q: _______________________________________________________________________
r : _______________________________________________________________________
The conjecture is (valid/invalid) _______________ based on the Law of
_______________.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-26
Holt McDougal Geometry
4. Converse: If an angle measures between
90° and 180°, then the angle is obtuse.
Reading Strategies
1. Conjecture: m∠BAC = m∠CAD
Biconditional: An angle is obtuse if and
only if it measures between 90° and 180°.
Hypothesis: Two angles are congruent.
valid, Detachment
5. No; sample answer: The switch could be
off.
2. Conjecture: If 90° < m∠S < 180°, then it
is not a right angle.
6. No; possible answer: Leap years have a
Feb. 29th.
p: The measure of ∠S is greater than 90°
and less than 180°.
7. A figure is a cube if and only if it is a
three-dimensional solid with six square
faces.
q: The angle is obtuse.
r: The angle is not a right angle.
valid, Syllogism
8. A person is a doofus if and only if the
person is Tanya’s younger brother.
2-4 BICONDITIONAL STATEMENTS AND
DEFINITIONS
Practice C
1. yes
Practice A
1. converse
2. No; the abnormal XXY male also has
exactly one Y chromosome.
2. q; p
3. If a cat is purring, then it is happy.
3. No; the abnormal XXY male also has a
pair of X chromosomes.
4. If a figure is straight and has two
endpoints, then it is a segment.
4. yes
5. Two angles share a side if and only if
they are adjacent.
6. Your temperature is normal if and only if it
is 98.6°F.
7. True; False; False; Sample answer: x = 4
5. Possible answer: Postulates are
statements that are accepted as true
without proof. Definitions are statements
that describe mathematical objects and
provide vocabulary for investigating these
objects.
8. True; False; False; Sample answer: It is
midnight.
6. postulate
7. definition
9. True
8. postulate
9. postulate
10. definition
Practice B
Reteach
1. Conditional: If the tea kettle is whistling,
then the water is boiling.
1. Conditional: If Lindsay takes photos for the
yearbook, then she doesn’t play soccer.
Converse: If Lindsay doesn’t play soccer,
then she will take photos for the yearbook.
Converse: If the water is boiling, then the
tea kettle is whistling.
2. Conditional: If a biconditional is true, then
the conditional and converse are both
true.
2. Conditional: If m∠ABC = m∠CBD, then
JJJG
BC is an angle bisector of ∠ABD.
JJJG
Converse: If BC is an angle bisector of
∠ABD, then m∠ABC = m∠CBD.
Converse: If the conditional and converse
are both true, then the biconditional is
true.
3. Converse: If each song costs $0.99, then
you can download 6 songs for $5.94.
Biconditional: You can download 6 songs
for $5.94 if and only if each song costs
$0.99.
3. Converse: If n − 1 is divisible by 2, then n
is an odd number.
Biconditional: n is an odd number if and
only if n − 1 is divisible by 2.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A13
Holt McDougal Geometry