Geometry
Reasoning in Algebra Section 2-4
Review: Naming Angles:
1. Use the diagram at the right to find the measure of each angle.
a) Name an angle that is a vertical angle to
b) Name the two angles whose sum is
c) Name an angle adjacent and congruent to
d)
is a supplement of what angle(s)?
e)
is a complement to what angle?
Section 2-4____________________________________________________________
Part I: Properties of Equality – Properties accepted as true in Algebra.
Addition Property:
Example: If
then ______________________________
Subtraction Property: Example: If
then _____________________________
Multiplication Property: Example :If
then ______________________________
Division Property:
then ______________________________
Example: If
Reflexive Property: Example: x = ____
Symmetric Property: Example: If
Transitive Property: Example: if
, then
.
and
, then
.
Substitution Property: Example: If x=52, then you can replace _____ with the value _____ in any expression.
Distributive Property: Example:
Part II: Properties of Congruence – True for measurable geometric Figures (segments, angles)
Reflexive Property: Example:
Symmetric Property: Example: If
Transitive Property: Example: If
or
, then __________≅_______________
and
, then ___________≅____________
Name the properties that justify each statement:
1.
3. If
, then
and
_____________
, then
Algebra Proofs: Give a reason for each step.
2. If
then
___________________________
______
Geometry
Reasoning in Algebra Section 2-4
1. Solve for x:
2. Solve for x:
1)
1. ______________
1)
1) _________
2)
2. ______________
2)
2) _______________
3)
3. ________________
3)
3) _______________
4)
4) _______________
3. Solve for x:
4. Solve for y:
1
1)________________
1)
1) ___________
2)
2)______________
2)
2)_______________
3)
3)______________
3)
3)_____________
4)
4)______________
4)
4)_______________
5
5)______________
5)
5)________________
Geometry Proofs: Give a reason for each step
5. Given
6. Given:
Find AB.
Find x.
1) AC=21
1) _______________
1)
2) AB+BC=AC
2)______________
2)
3)
3)___________
1)_____________
2)____
3)
3) __________
4)
4)________________
4)
4)___________
5)
5)________________
5)
5)___________
6) y = 6
6)________________
6)
6)___________
7) AB=12
7)________________
Geometry
7. Find
Reasoning in Algebra Section 2-4
.
8. Given:
bisects
Find x.
1)
1)______________
1)
bisects
1)________
2)
2) substitution_____
2)
2)________
3)
3)_______________
3)
3)__________
4) _____=________
4)______________
4) 40=2x
4)_________ 5) x =
_________
5)_______________
5) x=20
5)__________
6)
6)________________
CHALLENGE: Given: KL = 3PM. Find x and show steps.