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Day 7
Reasoning in Geometry (2)
Conditional and Related Statements
• Write a conditional statement and its
converse, its inverse and its
contrapositive.
Vocabulary:
Conditional Statement: a statement that can be
written as an if-then statement. (After “If”Hypothesis; After “Then”- Conclusion)
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(Ex)
If it’s rain, then Bonding Day is postponed.
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(Ex)
Two angles are supplementary if they are a linear
pair.
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Negation of a statement: the opposite of the original
statement.
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(Ex)
Original: It is snow.
Negation: It is NOT snow.
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(Ex)
Original: A right triangle has a right angle.
Negation: A right triangle does not have a right
angle.
Verifying Statement:
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Conditional Statements can be true or false. To show that a conditional
statement is true, you must prove that the conclusion is true every time
the hypothesis is true. To show that a conditional statement is false, you
need to give only one counterexample.
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(ex) Write a conditional statement and decide if it is true or false.
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(1) Congruent Segments have equal measures.
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(2) Supplementary angles form a linear pair.
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Related Conditional Statements
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Converse of a conditional statement: exchange
the hypothesis and the conclusion.
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Inverse of a conditional statement: negate both
hypothesis and the conclusion.
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Contrapositive or a conditional statement: Firstly
write the converse and then negate both the
hypothesis and the conclusion.
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(Ex) Write the converse, inverse and contrapositive of
given conditional statements. Decide if each
statement is true or false.
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(a) If m∠A = 99° , then
∠A is obtuse.
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(b) If a polygon is equilateral, then the polygon is regular.
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(c) If a figure is a square, then it has four right angles.
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Biconditional Statements: When a conditional
statement and its converse are both true, you can
write them as a single biconditional statement.
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(ex) Definition of Perpendicular Lines
Definition: if two lines intersect to form a right angle,
then they are perpendicular.
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Converse: If two lines are perpendicular, then they
intersect to form a right angle.
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Biconditional Statement: Two lines are perpendicular if
and only if they intersect to form a right angle.
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Practice: Write a converse, inverse and contrapositive
statement of each conditional statement. Then decide
if each is true or false.
(a) Linear Pair Conjecture:
If two angles form a linear pair, then the
measures of the angles add up to 180 degree.
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(b) Vertical Angles Conjecture:
If two angles are vertical angles, then they have
equal measures.
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With Deductive Reasoning, you use facts,
definitions, and properties to draw conclusions
and prove that conjectures are true.
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Given: Two lines are intersecting and form 4 angles.
Conjecture: ∠1 and ∠3 are vertical angles.
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Explain why.
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