Download intro to proofs with angle relations

Geometry
Unit 3: Angles and Lines – Beginnings of proofs!
Name:
One of the main goals in studying geometry is to develop your ability to reason critically, to draw valid
conclusions based upon observations and proven facts. Master detectives do this sort of thing all the time. In
geometry, we follow a similar deductive thought process.
Class Example
Recall the:
Now let’s use deductive reasoning to prove it!
Exterior angle Theorem for Triangles:
Notice that each step in the proof was justified by a
previously known or demonstrated fact. We end up
with a newly proven fact (that an exterior angle of
any triangle is the sum of the measures of the
opposite interior angles of the triangle). This
ability to identify the steps used to reach a
conclusion based on known facts is deductive
reasoning
Exercise 1: Prove that vertical angles are congruent.
Always make a plan!
1. What do you know about ∠𝑤 𝑎𝑛𝑑 ∠𝑥? What about ∠𝑧 𝑎𝑛𝑑 𝑦?
2. What conclusion can be drawn from the givens above?
3. Write out you proof:
Basic Property Reference Sheet
Now You Try!
1. Given the diagram at the right, prove 𝑚∠𝑤 + 𝑚∠𝑥 + 𝑚∠𝑧 = 180𝑜
(what do you know about angles x, y and z?)
2. Given the diagram to the right, prove 𝑚∠𝑤 = 𝑚∠𝑦 + 𝑚∠𝑧.
3. Given the diagram, prove 𝑚∠𝑥 + 𝑚∠𝑤 = 𝑚∠𝑦 + 𝑚∠𝑧.
(hint: label the missing angle as a and use it in your proof)
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ //𝐷𝐸
̅̅̅̅ , prove 𝑚∠𝐴𝐵𝐶 = 𝑚∠𝐸𝐷𝐶.
4. Given that ̅̅̅̅
𝐴𝐵 //𝐷𝐶
(what do you know about parallel lines and transversals?)
Geometry
Unit 2: Lines and Angles – Intro to proof! HW
Name:
1. In the diagram to the right, use the information to prove 𝑚//𝑛. Be sure and provide exact reasons for all
your claims!
2. In the diagram below, prove that the angles marked by the arrows sum to 360o.
(hint: label all the angles, use vertical angle thm and triangle angle sum)
̅̅̅̅ ⊥ 𝐸𝐹
̅̅̅̅ . (Don’t forget the reasons!) (and remember ⊥ = 90𝑜 )
3. Use the figure below to prove that 𝐷𝐶
Exit Ticket
Name:
In the diagram to the right, prove that the labeled angles sum to 180o.
Exit Ticket
Name:
In the diagram to the right, prove that the labeled angles sum to 180o.