Download Section 2-6 Proving Geometric Relationships With Solutions Gordon

Geometry
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Learning Objective: Students will use 3 different
methods to prove geometric relationships
(2 column proof, flowchart, and paragraph
form)
Learning Target 2A I can connect reasoning in
algebra and geometry by justifying steps in a
logical argument.
Geometry
2-6 Proving Geometric Relationships
Page 59
Prove the following using “Paragraph form”
(write underneath flowchart):
Prove the following using two columns
Flowchart proof, or flow proof
A proof which uses boxes and arrows to show
the flow of a logical argument.
Paragraph Proof
A proof which presents the statements and
reasons of a proof as sentences in a paragraph.
It uses words to explain the logical flow of the
argument.
Geometry
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Page 61
Theorem 2.3 Right Angles Congruence Theorem
All right angles are congruent.
Geometry
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Page 61
Theorem 2.4 Congruent Supplements Theorem
If two angles are supplementary to the same angle (or
to congruent angles), then they are congruent.
If ∠1 and ∠2 are supplementary and ∠3 and ∠2 are
supplementary then ∠1 ≅ ∠3.
Geometry
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Page 62
Theorem 2.5 Congruent Complements Theorem
If two angles are complementary to the same angle (or
to congruent angles), then they are congruent.
If ∠4 and ∠5 are complementary and ∠6 and ∠5 are
complementary then ∠4 ≅ ∠6.
Geometry
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Page 62
Postulate 2.8 Linear Pair Postulate
If two angles form a linear pair, then they are
supplementary.
∠1 and ∠2 form a linear pair so ∠1 and ∠2 are
supplementary and 𝑚∠1 + 𝑚∠2 = 180.
Geometry
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Page 62
Theorem 2.6 Vertical Angles Congruence Theorem
Vertical angles are congruent.
Geometry
Page 62
2-6 Proving
Geometric
POINTS,
LINES ANDRelationships
PLANES
Geometry
2-6 Proving Geometric Relationships
Not in book
Geometry
2-6 Proving Geometric Relationships
Not in book
Geometry
2-6 Proving Geometric Relationships
Not in book
Use the diagram and the given angle measure to find
the other three angle measures.
1. 𝑚∠1 = 117°.
Geometry
2-6 Proving Geometric Relationships
Not in book
Use the diagram and the given angle measure to find
the other three angle measures.
2. 𝑚∠2 = 59°.
Geometry
2-6 Proving Geometric Relationships
Not in book
Use the diagram and the given angle measure to find
the other three angle measures.
3. 𝑚∠4 = 88°.
Geometry
2-6 Proving Geometric Relationships
Not in book
Use the diagram and the given angle measure to find
the other three angle measures.
4. Find the value of w
Geometry
Prove that Vertical Angles are Congruent
Use the word bank below to prove the theorem.
∠1 & ∠2 are vertical angles
𝑚∠2 + 𝑚∠3 = 180
Segment Addition Postulate Substitution
Angle Addition Postulate
Given
Subtraction Property
Prove the Vertical Angles Theorem
Given: ∠1 and ∠2 are vertical
Prove: ∠1 ≅ ∠2
Statements
a.
c. 𝑚∠1 + 𝑚∠3 = 180
e.
g. 𝑚∠1 + 𝑚∠3 = 𝑚∠2 + 𝑚∠3
i. 𝑚∠1 = 𝑚∠2 or ∠1 ≅ ∠2
Reasons
b.
d.
f. Angle addition postulate
h.
j.