Download ANSWER CHECK test review

NAME ________________________________________________
DATE ______________________
PERIOD _______
REVIEW Unit 1 Test reasoning and proof
Use the figure to name each term using the appropriate symbols to designate.
1. plane
2. angle
3. point
plane A
point L
∠LTQ
4. line
5. ray
6. segment
𝑇𝐿
𝑇𝑄
𝑆𝑇
**** answers may vary ****
State the property of equality, property of congruence or postulate that justifies each statement.
7. If a + 7 = 20, then a = 13
8. If AB = CD and CD = EF, then AB = EF
subtraction property (=)
transitive property
𝑥
−6
If U is between T and V, then UV = UT + TV
segment addition postulate
12. If 4(x - 3) = 16, then 4x - 12 = 16.
distributive property
14. If ¾ = 0.75, then 0.75 = ¾.
symmetric property
16. If the m∠1 = 45 and m∠2 = 45, then m∠1 = m∠2.
substitution property (=)
= 2, then 𝑥 = −12.
multiplication property (=)
11. If 4x = -x + 20, then 5x = 20
addition property (=)
13. TP = TP
reflexive property
15. If 2BC = 2DE, then BC = DE
division property (=)
9. If
10.
Find the measure of each numbered angle and name the theorems that justify your work.
17.
m∠13 = 4x + 11
m∠14 = 3x + 1
18.
m∠2 = 4x - 26
m∠3 = 3x + 4
19.
m∠4 = 2x - 5
m∠5 = 4x - 13
m∠13 = 107
m∠14 = 73
m∠2 = 94
m∠3 = 94
m∠4 = 31
m∠3 = 59
supplementary thm
vertical angle thm
compl. thm, vert. angle
Find the value of x and state any theorems and/or postulates used to support your answer.
20.
21.
x = 14
y = 37
vert. angle, corresp,
alt. int
22.
x = 49 or maybe 28…?
y = 23
suppl, corresp, alt. int
x = 74
y = 37
z = 25
corresponding, suppl.
Find x so that l || m . Identify the postulate or theorem you used.
23.
24.
x = 12
corresponding
25.
x = 21
alternate exterior
x=9
alternate interior
Using the diagram, give the reason that justifies each statement.
definition of supplementary or
26. ∠𝑊𝑅𝑋 + ∠𝑍𝑅𝑋 = 180
linear pair
27. ∠𝑊𝑅𝑌 + ∠𝑌𝑅𝑍 = ∠𝑊𝑅𝑍
angle additon postulate
28.
If 𝑅𝑋 ⊥ 𝑅𝑌, then ∠𝑋𝑅𝑌 is a right angle.
29.
If R is the midpoint of 𝑊𝑍, then 𝑊𝑅 ≅ 𝑅𝑍.
30.
If 𝑅𝑌 bisects ∠𝑍𝑅𝑋, then ∠𝑌𝑅𝑋 ≅ ∠𝑌𝑅𝑍.
definition of perpendicular
midpoint theorem
angle bisector theorem
Complete each statement.
31.
Two angles whose measure add up to 90° are ________________________.
commplementary
32.
consecutive interior angles
If 2 parallel lines are cut by a transversal, _______________________
are not necessarily congruent.
33.
Two angles whose measure add up to 180° are
34.
Two angles are congruent if they are ______________________.
vertical
35.
alternate interior
__________________________
are the pair of angles created inside parallel lines,
located on opposite sides of the transversal cutting the parallel lines.
supplementary
Fill in the missing steps and justifications.
36.
Given: -6(2x + 1) + x = 16
Prove: x = -2
STATEMENTS
a. -6(2x + 1) + x = 16
b. -12x - 6 + x = 16
c. -11x - 6 = 16
d. -11x - 6 + 6 = 16 + 6
e. -11x = 22
f. -11x/-11 = 22/-11
g. x = -2
REASONS
f.
g.
given
distributive property
subs or simplify
addition prop (=)
subs or simplify
division prop (=)
subs or simplify
a.
given
b.
def of congruent segments
def of midpoint
segment addition
subs property
subs property
simplify
division property (=)
def of congruent segments
a.
b.
c.
d.
e.
37.
a.
b.
c.
d.
e.
f.
g.
h.
i.
STATEMENTS
C is the midpoint of AE.
C is the midpoint of BD.
AE ≅ BD
AE = BD
AC = CE, BC = CD
AC + CE = AE, BC + CD = BD
AC + CE = BC + CD
AC + AC = CD + CD
2AC= 2CD
AC = CD
AC ≅ CD
REASONS
c.
d.
e.
f.
g.
h.
i.
WORD BANK
congruent
complementary
consecutive interior
vertical
alternate interior
supplementary
adjacent
38.
39.
40.
Given: ∠1 ≅ ∠3 and AC ∥ BD
Prove: A𝐵 ∥ CD
STATEMENTS
a. ∠1 ≅ ∠3, AC || BD
b. ∠2 ≅ ∠3
c. ∠1 ≅ ∠2
d. AB || CD
Given: FL = AT
Prove: FA = LT
STATEMENTS
a. FL = AT
b. LA = LA
c. FL + LA = AT + LA
d. FL + LA = FA
AT + LA = LT
e. FA = LT
a.
b.
c.
d.
REASONS
given
corresponding angle post.
transitive postulate
if alt angles are ≅, then lines are ||
REASONS
given
b. reflexive
c. addition property of =
d. segment additon property
a.
e.
Given: ∠1 ≅ ∠3
Prove: ∠1 ≅ ∠4
STATEMENTS
substitution
REASONS
a. ∠1 ≅ ∠3
a.
b. ∠3 ≅ ∠4
c. ∠1 ≅ ∠4
b.
c.
given
vertical angles are congruent
substitution