Download no mixed numbers, rounded decimals or repeating

Geometry PreAP/IB
A #_____________
Name:____________________________________________per:_____
Review #1 for Test 2
NO MIXED NUMBERS, ROUNDED DECIMALS OR REPEATING DECIMALS
1. Conditional Statement: If two angles are adjacent, then they have a common side.
Converse:__________________________________________________________________________________
______________________________________________________________________________________________
Inverse:____________________________________________________________________________________
______________________________________________________________________________________________
Contrapositive: ____________________________________________________________________________
______________________________________________________________________________________________
T or F
T or F
T or F
T or F
2. If 𝑚∠𝐴 = 63o, then ∠𝐴 is an acute angle. The conditional statement is TRUE or FALSE. (CIRCLE ONE)
Write the converse: _____________________________________________________________________________ TRUE / FALSE
3. _________________________If 3x – 15 is the measure of an acute angle, what restrictions are placed on x?
4. Find: GJ = ______________________
̅̅̅̅ ≅ 𝐽𝐾
̅̅̅ , GH = x + 10
Given: 𝐺𝐻
HJ = 8, JK = 2x – 4
5. ∠𝑇and ∠𝑌𝑋𝑇 are complementary; ∠𝑌𝑅𝑆 ≅ ∠𝑌𝑋𝑇;
m∠𝑇 = 𝑥 + 𝑦; m∠𝑌𝑋𝑇 = 4𝑦 + 2; 𝑚∠𝑌𝑅𝑆 = 2𝑥 − 6; m∠𝑃𝑅𝑆 = 100
SHOW ALGEBRA to solve for x = _______ & y = ________
Does ⃗⃗⃗⃗⃗
𝑅𝑋bisect ∠𝑃𝑅𝑆? __________ EXPLAIN:
6. Find the measures of each of the following angles in terms of x and y.
a. ∠𝐻𝐹𝐾_______________
b. ∠𝐸𝐹𝐾_______________
c. ∠𝐻𝐹𝐺_______________
⃗⃗⃗⃗⃗⃗ bisects ∠𝑅𝑆𝑇 and 𝑚∠𝑅𝑆𝑇 = 108. 𝑆𝑍
⃗⃗⃗⃗ bisects ∠𝑅𝑆𝑊, 𝑆𝑃
⃗⃗⃗⃗ bisects ∠𝑅𝑆𝑍 and 𝑆𝑅
⃗⃗⃗⃗⃗ bisects
7. 𝑆𝑊
∠𝑁𝑆𝑃. Sketch a diagram and find m∠𝑅𝑆𝑃 and 𝑚∠𝑁𝑆𝑃.
m∠𝑅𝑆𝑃=_____________________
𝑚∠𝑁𝑆𝑃=________________________
Show Algebra on the following problems. (Literally translate the word problem into an equation first)
8. _______________ _______________ The measure of the complement of ∠𝐴 is five times the measure of ∠𝐴.
Find the measure of ∠𝐴 and its complement.
9. _______________ _______________ The measure of the supplement of ∠𝐵 is 17 times the measure of ∠𝐵.
Find the measure of ∠𝐵 and its complement.
10. _______________The sum of the measures of a complement and a supplement of an angle is 184°. Find
the measure of the angle.
11. ______________The measure of ∠A is twice the measure of ∠B and the measure of ∠B is twice the measure of
∠C. If ∠A and ∠C are supplementary, find the measure of ∠B.
WRITE THE REASON FOR EACH STATEMENT.
12. Given: ∠DEB and ∠EBT are right angles, ∠1 ≅ ∠4
Prove: ∠2 ≅ ∠3
Statements
Reasons
1. ∠DEB and ∠EBT are right angles. 1. ___________________________________
2. 𝑚∠DEB= 90
2.___________________________________
𝑚∠EBT = 90
3. 𝑚∠DEB =𝑚∠EBT
3.___________________________________
4. 𝑚∠1 + 𝑚∠2 = 𝑚∠𝐷𝐸𝐵
4.___________________________________
𝑚∠3 + 𝑚∠4 = 𝑚∠𝐸𝐵𝑇
5. 𝑚∠1 + 𝑚∠2 = 𝑚∠𝐸𝐵𝑇
5. ___________________________________
6. 𝑚∠1 + 𝑚∠2 = 𝑚∠3 + 𝑚∠4
6. ___________________________________
7. ∠1 ≅ ∠4
7. ___________________________________
8. 𝑚∠1 = 𝑚∠4
8. ___________________________________
9. 𝑚∠1 + 𝑚∠2 = 𝑚∠3 + 𝑚∠1
9.____________________________________
10. 𝑚∠2 = 𝑚∠3
10.___________________________________
11. ∠2 ≅ ∠3
11.___________________________________
13. Given: ∠1 and ∠2 are complementary
Prove: ∠𝐴𝑋𝐶 is a right angle
Statements
1. ∠1 and ∠2 are complementary
Reasons
1. __________________________
2. 𝑚∠1 + m∠2 = 90
2.___________________________
3. 𝑚∠1 + m∠2 = 𝑚∠𝐴𝑋𝐶
3. ___________________________
4. m∠𝐴𝑋𝐶 = 90
4.____________________________
5. ∠𝐴𝑋𝐶 is a right angle
5. ___________________________
14. Given: 𝑚∠1 = 𝑚∠3; 𝑚∠2 = 𝑚∠4
Prove: 𝑚∠𝐴𝐵𝐶 = 𝑚∠𝐷𝐸𝐹
Statements
1. 𝑚∠1 = 𝑚∠3; 𝑚∠2 = 𝑚∠4
Reasons
1. ___________________________________
2. 𝑚∠1 + 𝑚∠2 = 𝑚∠3 + 𝑚∠4
2.___________________________________
3. 𝑚∠1 + 𝑚∠2 = 𝑚∠𝐴𝐵𝐶
3.___________________________________
𝑚∠3 + 𝑚∠4 = 𝑚∠𝐷𝐸𝐹
4. 𝑚∠1 + 𝑚∠2 = 𝑚∠𝐷𝐸𝐹
4.___________________________________
5. 𝑚∠𝐴𝐵𝐶 = 𝑚∠𝐷𝐸𝐹
5. ___________________________________
INDICATE THE LETTER ASSIGNED TO THE PROPERTY, POSTULATE, THEOREM OR DEFINITION THAT JUSTIFIES
THE GIVEN STATEMENT, REFERECING THE GIVEN DIAGRAM. YOU MAY USE AN ASWER MORE THAN ONCE.
A.
A. SEGMENT ADDITION
B. DEFINITION OF MIDPOINT
C. DEF. OF SEGMENT BISECTOR
D. DEF. OF CONGRUENT SEGMENTS
E. ANGLE ADDITION
F. ANGLE ADDTION PART 2
G. DEFINITION OF ANGLE BISECTOR
H. DEF. OF CONGRUENT ANGLES
I. DEFINITION OF RIGHT ANGLE
J.
K.
L.
M.
N.
O.
P.
Q.
R.
ADDITION/SUBTRACTION OF =
MULTIPLICATION/DIVISION OF =
DISTRIBUTIVE
SUBSTITUTION OF =
REFLEXIVE OF =
REFLEXIVE OF ≅
SYMMETRIC OF =
SYMMETRIC OF ≅
TRANSITIVE OF =
S.
T.
U.
V.
W.
TRANSITIVE OF ≅
MIDPOINT THEOREM
ANGLE BISECTOR THEOREM
VERTICAL ANGLE THEOREM
DEF. OF COMPLEMENTARY ∠s
X.
Y.
Z.
DEF. OF SUPPLEMENTARY ∠s
LINEAR PAIR THEOREM
COMBINE LIKE TERMS
̅̅̅̅ , then 𝐷𝐼
̅̅̅ bisects 𝐵𝐹
̅̅̅̅ .
15. __________ If E is the midpoint of 𝐵𝐹
16. ___________ 𝑚∠5 + 𝑚∠6 = 𝑚∠𝐷𝐾𝐺
17. ___________ If 3𝑥 − 4 = 2, then 3𝑥 = 6.
18. ___________ If HB = 45 and EK +KH = HB, then EK +KH = 45.
19. ___________ ∠2 ≅ ∠1
1
̅̅̅̅ is the bisector of ∠𝐸𝐾𝐺, then 𝑚∠6 = 𝑚∠𝐸𝐾𝐺.
20. ___________ If 𝐾𝐹
2
21. ___________ If K is the midpoint of ̅̅̅
𝐽𝐺 , then ̅̅̅
𝐽𝐾 ≅ ̅̅̅̅
𝐾𝐺 .
22. ___________ 𝑚∠5 + 𝑚∠𝐹𝐾𝐼 = 180
23. ___________ If ∠4 ≅ ∠5 and ∠4 ≅ ∠6, then ∠6 ≅ ∠5.
24. ___________ If 2(𝑥 + 5) = 10, then 2𝑥 + 10 = 10.
25. ___________ If 2𝑥 + 3𝑦 + 5𝑥 = 20 + 2, then 7𝑥 + 3𝑦 = 22.
̅̅̅̅ is the bisector of ∠𝐸𝐾𝐽, then ∠3 ≅ ∠4.
26. ___________ If 𝐾𝐶
27. ___________ If BE=5 and BE+EF=BF, then 5+EF=BF.
28. ___________ If BK = KF, then ̅̅̅̅
𝐵𝐾 ≅ ̅̅̅̅
𝐾𝐹 .
29. ___________ ∠𝐹 ≅ ∠𝐹
̅̅̅, then K is the midpoint of 𝐷𝐼
̅̅̅.
30. ___________ If ̅̅̅
𝐽𝐾 is the bisector of 𝐷𝐼
31. __________ If ∠4 ≅ ∠5, then 𝑚∠4 = 𝑚∠5.
32. ___________ ∠3 and ∠𝐵𝐾𝐺 are supplementary
33. ___________ If 𝑚∠5 + 𝑚∠6 = 90, then ∠5 and ∠6 are complementary.
34. ___________ If 𝑚∠3 + 𝑚∠𝐵𝐾𝐺 = 180, then ∠3 and ∠𝐵𝐾𝐺 are supplementary.