Name ________________________
Date ____________
Geometry – Review for Quarterly #1 Test
Period __________
1. Name two lines in plane R.
H
●
2. Name the intersection of plane R and ⃡𝑀𝑉 .
L
●
3. Name the intersection of ⃡𝐻𝑇 and ⃡𝐿𝐴.
M
U
●
R
A
●
T
●
V
4. Draw and label a pair of opposite rays 𝐴𝐵 and 𝐴𝐶 .
̅̅̅̅ .
5. Find the length of 𝑍𝑌
6. K is between M and N. MK = (3y), KN = 17, and MN = (5y + 9). Find MN.
M
●
K
●
N
●
7. E is the midpoint of ̅̅̅̅
𝐷𝐹 , DE = (2x + 4) and EF = (3x – 1). Find DE, EF, and DF.
8. Find the measure of ∠DOB. Then, classify the angle as acute, right, or obtuse.
1
9. m∠ABC = 115° and m∠ABD = 85°. Find m∠DBC.
A●
●D
●
B
●
C
10. 𝐵𝐷 bisects ∠ABC, m∠ABD = (6x + 4)°, and m∠DBC = (8x - 4)°. Find m∠ABD and m∠DBC.
A
●
●
D
●
B
●
C
11. 𝐵𝐷 bisects ∠ABC, m∠ABC = (6x + 10)°, and m∠ABD = (2x + 8)°. Find m∠DBC.
A
●
●
D
●
B
●
C
12. Tell whether the following pairs of angles are only adjacent, adjacent and form a linear pair, or not
adjacent.
5
4
3
a. ∠3 and ∠4
1
2
b. ∠1 and ∠2
c. ∠5 and ∠2
13. Find the perimeter and area for each of the following shapes.
a. square with side 7 cm
b. rectangle with length 4 ft and width 2 ft
2
14. Find the circumference of a circle if its area is 25 yd2.
15. The area of a triangle is 16 m2. Find the height if the base is 8 m.
16. Find x.
(4y + 1)°
(2y – 7)°
17. Find x.
(7x – 32)° (3x + 12)°
18. Find x.
(3x + 20)°
(5x)°
19. Find the measure of the complement of ∠A, where m∠A = 47°.
20. Given ∠A and ∠B are supplementary and m∠A = (5x)° and m∠B = (15x – 10)°. Find the measure
of each angle.
21. An angle is 3 more than 2 times its complement. Find the measure of the angle.
22. Find the next number in the pattern: 2, 3, 5, 8, 12, _____
23. Complete the conjecture: The product of two negative numbers is ________________.
3
24. Identify each transformation.
a.
b.
c.
25. Translate the image. (x, y)  (x + 3, y – 2).
26. Given X(6, –8) and Y(4, –3).
̅̅̅̅
a. Find the midpoint of 𝑋𝑌
𝑥1 + 𝑥2 𝑦1 + 𝑦2
(
,
)
2
2
27. Write a justification for each step.
Given: m∠ABC = m∠DBE
Prove: x = 8
d = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
̅̅̅̅
b. Find the distance of 𝑋𝑌
●A
(2x +40)°
●C
Statements
1. m∠ABC = m∠DBE
1.
2. 2x + 40 = 5x + 16
2.
3. 40 = 3x + 16
3.
4. 24 = 3x
4.
5. 8 = x
5.
6. x = 8
6.
D
●
●
B
(5x + 16)°
●
E
Reasons
4
28. Identify each property, definition, or postulate.
a. If AB = CD and CD = EF, then AB = EF. __________________________________________
b. If m∠A = 90°, then ∠A is a right angle. ___________________________________________
c. If 2x – 5 = 20, then 2x = 25. ____________________________________________________
d. If 3x = 8, then 8 = 3x. _________________________________________________________
e. If 𝐴𝐵 bisects ∠CAT, then ∠CAB  ∠BAT. _________________________________________
f. 2(x + 3) = 2x + 6 _____________________________________________________________
g. x = x ______________________________________________________________________
h. Given B is between A & C, AB + BC = AC. ________________________________________
i. Given B is in the interior of ∠CAT, then m∠CAB + m∠BAT = m∠CAT. __________________
29. Solve and justify each step.
1. 5x – 3 = 4(x + 2)
1.
2.
2.
3.
1.
𝑧−3
2
= 10
1.
2.
2.
3.
3.
3.
4.
4.
X
30. Write a justification for each step.
(4n + 5)°
Given: m∠ABX + m∠XBC = 180°
Prove: n = 15
A
Statements
1. m∠ABX + m∠XBC = 180°
1.
2. 4n + 5 + 8n – 5 = 180
2.
3. 12n = 180
3.
4. n = 15
4.
(8n – 5)°
B
C
Reasons
5
31. If a figure is a right triangle with sides a, b, and c, then a2 + b2 = c2.
Hypothesis ______________________________________________________________________
Conclusion ______________________________________________________________________
Converse________________________________________________________________________
_______________________________________________________________________________
Bi-conditional ____________________________________________________________________
________________________________________________________________________________
Is the original conditional True or False?
Is the converse True or False?
If either is “False,” give a counterexample. ______________________________________________
_______________________________________________________________________________
Tell whether the reasoning process is deductive or inductive reasoning:
32. Ramon noticed that spaghetti had been on the school menu for the past five Wednesdays.
Ramon decides that the school always serves spaghetti on Wednesday. ___________________
33. Kyle did his assignment, adding the lengths of the sides of triangles to find the perimeters.
Noticing the results for several equilateral triangles, he guesses that the perimeter of every
equilateral triangle is three times the length of a side. ______________________
34. By using the definition of equilateral triangle (a triangle with three congruent sides) and of
perimeter (the sum of the lengths of the sides of a figure), Katie concludes that the perimeter of
every equilateral triangle is three times the length of a side. _________________
6