Download 160929-proofs-quiz-review

Name
September 29, 2016
Math 2 quiz review assignment
page 1
Geometric proofs: recap and practice
At our next class on Friday 9/30, we will have a half-period quiz on geometric proof.
Review outline: what we have so far
Proof writing styles and strategies


two-column proofs, flowchart proofs, and paragraph proofs
turning statements into if-then statements, identify what’s given and what’s to be proved
Facts (definitions)

all the definitions of commonly used geometry to date (see handout)
o angle bisector, median, altitude, perpendicular bisector, midpoint, square,
perpendicular, supplementary, straight angle, bisect, isosceles, equilateral,
equiangular, rhombus, congruence (CPCTC), Rotation around a point is 360 and
so on.
Facts we’ve assumed (postulates)




many algebra properties and rules
o addition property, subtraction property, reflexive property, transitive property,
substitution property
Angle Addition
Segment Addition
triangle congruence methods: SSS, SAS, ASA, AAS, HL
Facts we’ve proved (theorems)






Vertical Angle Theorem
Perpendicular Bisector Theorem and its converse (PBT and CPBT)
Isosceles Triangle Theorem and its converse (ITT and CITT)
Equilateral triangles must be equiangular; equiangular triangles must be equilateral.
Supplements of congruent angles are congruent
Congruent, supplementary angles are equal to 90
Skills needed for the quiz:




drawing and marking a diagram with the given information
writing a converse of a statement
idenitfy the given and prove from a general statement and make it specific to a daigram
write clear and convincing arguments in any of the styles studied
o write triangle congruence proofs
o use triangle congruence as a step towards proving other things
o applying ITT and CITT as well as PBT and CPBT
Name
September 29, 2016
Math 2 quiz review assignment
page 2
Practice problems
1.
Given:
bisects
Prove:
is a median.
.
is isosceles
Complete this proof without using the reflexive property in your
proof.
2.
Read the paragraph proof below and edit it. There are errors to correct. You may state
the errors and the corrections in list form, or you can rewrite the proof correctly in any
form you like.
B
Given:
Prove:
,
A
C
E
D
Because
,
,
by SSS. Since the large triangles are
congruent their corresponding parts are congruent. Also,
because it is the
same side. So
by SAS; therefore
by CPCTC.
Name
September 29, 2016
3.
Math 2 quiz review assignment
page 3
G
Given: A is the midpoint of FG
A
3
1
Ð1@ Ð3
AB @ AC
F
2
Prove: BF @ CG
B
4. Given: AED is the
bisector of
C
A
Prove:
E
B
D
C
Name
September 29, 2016
5.
Math 2 quiz review assignment
page 4
Consider the statement: The medians of congruent triangles are congruent.
a. Write the statement in if-then form.
b. Create a labeled diagram that illustrates the given situation
c. Write given and prove statements that refer specifically to your labeled diagram (i.e.
using the letters you have chosen etc.)
d. Write the proof.
Name
September 29, 2016
6.
Given: A
2
1
C
Prove: AB
CD
Math 2 quiz review assignment
page 5
A
7. Given:
X
Y
Prove:
Z
C
B