Download 3.5 One Step Proofs

Geometry
Ms. Brinkman
3.5 One Step Proofs
Skills to Acquire
 Identify parts of a circle: center, angle measures of circles, and arcs.
 Recognize rotations and characteristics of rotations.
 Apply circle properties to real-world situations.
Review Problem:
1. Define a Proof: A sequence of procedures, starting with a hypothesis (antecedent) and ending with
the conclusion (consequent)
2. What is a justification? The reasoning (or property) used to go from one step to the next.
3. A proof must always have GIVEN information, and we are always trying to justify statements to come
to a logical conclusion.
4. Example: If 4r – 3 = 11, then r = 3.5
 Given: 4r – 3 = 11
 Conclusion: r = 3.5
Statement
Reason
4r – 3 = 11
Given
4r = 14
Addition Property of Equality (3 added to
both sides)
r = 3.5
Multiplication Property of Equality
(both sides multiplied by ¼)
5.
What is a midpoint? The center (middle) point on a segment that is equal distance from 2
endpoints.
6. Draw line segment AB. Put C where you think the midpoint of the segment should be. Use "tick
marks" to show equality.
A
C
B
7. Given C is a midpoint above, what do we know? We know that AC = CB and AC + CB = AB
8. Why do we know this is true? The definition of a MIDPOINT!
9. Given Circle A with points B & C on the circle. Draw this!
B
A
C
 Prove: AB is congruent to AC. Why are they congruent? Definition of a circle (each point on circle is
equidistant from center point)
10. Draw two lines that intersect and identify the four angles as angles 1, 2, 3,& 4 in a clockwise manner.
2
1
3
4
11. Why is angle 1 congruent to angle 3? Vertical Angle Theorem How do you know this? Vertical angles
are congruent. Both share angle 2. Since angles 1 and 2, and 2 and 3 are supplementary, then 1
and three must be congruent.
12. Given ∠RPS and ∠RPU
are a linear pair.
Statement
∠RPS and ∠RPU
are a linear pair.
Conclusion: ∠RPS and ∠RPU
are supplementary
U
R
P
T
S
∠RPS and ∠RPU
are supplementary
Reason
Given
Linear Pair Theorem
(or definition of linear pair)