Download Section 2-5 Proving Statements With Solutions Gordon

Geometry
2-5 Proving
Statements
POINTS,
LINES AND about
PLANES
Segments & Angles
How can you describe, identify
and apply the fundamental elements of parallel,
perpendicular and skew lines and prove their
relationships.
Learning Objective: Students will write two
column proofs, name and prove properties of
congruence.
Learning Target 2A I can connect reasoning in algebra and
geometry by justifying steps in a logical argument.
Geometry
2-5 Proving Statements about
POINTS,
LINES
AND
PLANES
Segments & Angles
Page 56
In your own words, write the meaning of each
vocabulary term.
proof
two-column proof
theorem
Geometry
2-5 Proving
Statements
POINTS,
LINES AND about
PLANES
Segments & Angles
Page 56
Theorem 2.1 Properties of Segment Congruence
Segment congruence is reflexive, symmetric & transitive.
Reflexive
For any segment AB, 𝐴𝐵 ≅ 𝐴𝐵
Symmetric If 𝐴𝐵 ≅ 𝐶𝐷, then 𝐶𝐷 ≅ 𝐴𝐵
Transitive
If 𝐴𝐵 ≅ 𝐶𝐷 and 𝐶𝐷 ≅ 𝐸𝐹, then 𝐴𝐵 ≅ 𝐸𝐹
Geometry
2-5 Proving Statements about
POINTS, LINES AND PLANES
Segments & Angles
Page 56
Theorem 2.2 Properties of Angle Congruence
Angle congruence is reflexive, symmetric & transitive.
Reflexive
For any angle A, ∠𝐴 ≅ ∠𝐴
Symmetric If ∠𝐴 ≅ ∠𝐵, then ∠𝐵 ≅ ∠𝐴
Transitive
If ∠𝐴 ≅ ∠𝐵 and ∠𝐵 ≅ ∠𝐶, then ∠𝐴 ≅ ∠𝐶
Geometry
2-5 Proving Statements about
POINTS,&
LINES
AND PLANES
Segments
Angles
Page 57
Writing a Two-Column Proof
Copy or draw diagrams and
label given information to help
develop proofs,
Geometry
2-5 Proving Statements about
POINTS,&
LINES
AND PLANES
Segments
Angles
Writing a Two-Column Proof
Complete the proof.
Geometry
2-5 Proving Statements about
POINTS,&
LINES
AND PLANES
Segments
Angles
Writing a Two-Column Proof
Given: ∠𝐷𝐵𝐺 = 3𝑥 + 2,
∠𝐺𝐵𝐸 = 5𝑥 − 8, and
𝑚∠𝐷𝐵𝐸 = 50°.
Prove: 𝑥 = 7
Geometry
2-5 Proving
Statements
POINTS,
LINES ANDabout
PLANES
Segments & Angles
Page 58
In Exercises 3 and 4, name the property that
the statement illustrates.
3.
If RST  TSU and TSU  VWX , then RST  VWX .
4.
If GH  JK , then JK  GH .
Geometry
2-5 Proving
Statements
POINTS,
LINES ANDabout
PLANES
Segments & Angles
Given: M is the midpoint of
Prove: MT  RS  SM
STATEMENTS
RT
REASONS
Page 58