GUADALUPE TELETOR
Name____________________________________
Geometry Semester 1 Exam Review
Chapter 1 Problems
Use the diagram to name each of the following.
1. Three non-collinear
2. Three collinear points DBE
points FAD
3. Four non-coplanar points AEBD
4. Two intersecting lines
5. Two Opposite Rays
⃡
6. Two names for ED
7. Another name for ∠DBA.
Determine if each group of points are coplanar:
8. Q, A, T and S
9. R, B, C, and S
10. T, A, Q and D
11. What is the intersection of planes AQR and TAQ?
(Do Not Forget Titles and Symbols)
Use the number line for 12-13.
12. What is AD?
Find the distance between the points below.
14. A(2, 5) and B(3, 9)
̅̅̅̅ and AB
̅̅̅̅ congruent
13. Are CA
d=
( x2 − x1 ) + ( y2 − y1 )
2
15. A (-3, 1) and B (1, -1)
Find the midpoint of a line segments with endpoints below. M= (
16. (-12, 18) and (-9, -21)
2
𝑥1+𝑥2 𝑦1 +𝑦2
2
,
2
)
17. (4, 10) and (6, -4).
Find the missing value.
18.
19.
1
Name each angle pair (a and b) as complementary, supplementary, linear pair, vertical or adjacent. (Some
may have more than one name.) Then tell if there is anything special about the angles (Congruent? Total?)
20.
21.
22.
23.
Determine whether each angle pair is complementary, supplementary, or neither.
24. 135 and 45
25. 55 and 25
26. 37 and 143
27. 62 and 28
Find the value of b in each of the following.
28.
29.
30.
32.
33.
Solve for x in each of the following.
31.
34. BT bisects ABC. Solve for x.
35. Use the diagram to solve for
the missing measures.
2
Chapter 2 Problems
Underline the hypothesis once and the conclusion twice for each of the following Conditional Statements.
1. If a triangle is equilateral, then it has three sides of equal length.
2. A polygon is a quadrilateral, If a polygon has four sides.
Predict the next number in the patterns:
3.
-2, -1, 1, 4, ___________, __________, …
4. 10, -20, 30, -40, ___________, __________, …
5. For the conditional statement below, write the converse, inverse, and contrapositive and
biconditional. For each, state whether true or false.
Conditional: If 2x + 2 = 8, then x = 3.
Converse:
Inverse:
Contrapositive:
Bi-Conditional:
If possible, make a conclusion from the given true statements.
6. Use deductive reasoning to make a conclusion. If a parallelogram has 4 congruent sides, then the
parallelogram is a rhombus. Parallelogram ABCD has 4 congruent sides.
Conclusion:
7. If a triangle is a right triangle, then the triangle has one 90° angle. ΔABC is a right triangle.
Conclusion:
8. If it is Tuesday, then the cafeteria is serving meat loaf. When the cafeteria serves meat loaf, Harlan
brings a sack lunch. Conclusion:
9. Which type of reasoning follows fact and logical reasoning? (Inductive or Deductive)
10. Which type of reasoning is based on patterns? (Inductive or Deductive)
State whether each of the following use Inductive or Deductive reasoning?
11. You can get your permit when you turn 15. Martina Just turned 15, so
she can get her permit.
12. My neighbor has cut his grass every Wednesday for the last 5 weeks.
I conclude that he will cut his grass this Wednesday, too.
3
Find a counterexample for each statement.
13. All numbers over 11 are composite
14. All odd numbers are prime.
15. All birds can fly.
16. When you add two numbers, you always get a
positive answer.
17. Use the diagram to determine whether each statement is true or false.
a. Points R, S, and T are coplanar.
______
b. UTR and UTW are complementary.
______
c. Points R, S, and T lie on the same line.
______
d. TS is parallel to RS.
______
e. VTS and UTX are supplementary.
______
R
U
T
S
V
X
W
18. Match each statement with the property of equality.
19.
_____ If JK = PQ and PQ = ST, then JK = ST
A. Addition Property
_____ If B = C, then B + A = C + A
B. Reflexive Property
_____ AB = AB
C. Substitution Property
_____ If AB = CD, then AB – EF = CD – EF
D. Transitive Property
_____ If x = 4 and y = x + 5, then y = 9
E. Symmetric Property
_____ If m∠P = m∠Q, then m∠Q = m∠P
F. Subtraction Property
Given : AB  BC , BC  CD
Prove : x = 5
Statements
Reasons
1. AB  BC , BC  CD
1.
2. AB  CD
2.
3. AB = CD
3.
4. 6x + 15 = x + 40
4.
5. 5x + 15 = 40
5.
6. 5x = 25
6.
7. x = 5
7.
4
20. Solve and write a reason for each step.
5x + 10 = 3x + 28
21. MULTIPLE CHOICE: Which is the following justifies the statement: “AB + BD = AD”?
a) Linear Pair Postulate
c) Addition POE
e) Substitution POE
b) Segment Addition Postulate
d) Vertical Angle Theorem
A
B
D
C
E
22. Complete each statement given that
mAQG = 90°, mBQC = 60°, and mCQD = 30°
a. mAQB = _______
b. mCQA = _______
c. mEQF = _______
d. mDQG = _______
e. mCQG = _______
Chapter 3 Problems
Name the line or lines that fit the descriptions:
1. parallel to GC .
2. perpendicular to EF .
3. skew to HD .
4. a plane that is parallel to plane AEF
Complete the statement with the correct angle, Then tell if they are congruent (≅) or supplementary (180°)
when lines are parallel.
5.
 3 and  _______ are Corr. ∠’s. They are __________.
6.
 4 and  _______are Same Side Interior. They are__________.
7.
 8 and  _______are Alternate Exterior. They are___________.
8.
 5 and  _______ are Corr. ∠’s. They are __________.
9.
 3 and  _______ are Alternate Interior. They are __________.
1
2
4 3
5 6
8 7
10.  1 and  _______ are Same Side Exterior. They are___________.
5
Find the missing value.
11.
12.
13.
15.
16.
Solve for x.
14.
Decide if a//b. If yes, choose the appropriate reason from the box.
17. ∠2 ≅ ∠6
a
18. ∠3 ≅ ∠2
m=
y2 − y1
x2 − x1
Corr. ∠’s Converse
AIA Converse
AEA Converse
SSIA Converse
SSEA Converse
19. ∠1 ≅ ∠8
20. m∠3 + m∠5 = 180
b
21. m∠1 + m∠7 = 180
Write the slope for each of the following pairs of equations. Then decide whether the two lines listed below
are PARALLEL, PERPENDICULAR, OR NEITHER.
22. 𝑦 = 𝑥 − 4 𝑎𝑛𝑑 𝑦 = 𝑥 + 6
m = _______
m = _______
________________________________
24. 𝑦 = 2𝑥 − 5 𝑎𝑛𝑑 𝑦 = −2𝑥 + 1
m = _______
m = _______
________________________________
1
23. 𝑦 = − 3 𝑥 − 3
m = _______
𝑎𝑛𝑑 𝑦 = 3𝑥 + 2
m = _______
________________________________
25. 𝑦 = −5𝑥 − 1 𝑎𝑛𝑑 𝑦 = −5𝑥 + 5
m = _______
m = _______
______________________________
6
𝟑
Write an equation of a line parallel and perpendicular to 𝒚 = 𝟒 𝒙 + 𝟏 with each new y-intercept below.
26. y-intercept: -3
27. y-intercept: 0
29.
28. y-intercept: 5
Statements
3
Word Bank: Corr. ∠’s, Given, Transitive, AEA,
AIA, (One Not Used)
Reasons
1. l//m, p//q
1.
2. ∠1 ≅ ∠3
2.
3. ∠3 ≅ ∠2
3.
4. ∠1 ≅ ∠2
4.
Statements
30. Given: j//k, m1 = 50
Prove: m4 = 130
4
Word Bank: AEA, Given, Transitive, AIA,
Linear Pair Postulate (LPP), Subtraction,
Def. of ≅, AIA, Substitution,
(one not used)
Reasons
1. j || k , m1 = 50
1.
2. ∠1 ≅ ∠3
2.
3. m∠1 = m∠3
3.
4. m∠3 = 50°
4.
5. m∠3 + m∠4 = 180°
5.
6. 50 + m∠4 = 180°
6.
7. m∠4 = 130°
7.
Chapter 4 Problems
Name the transformation that maps the un-shaded figure onto the shaded figure (Translation,
Reflection, Rotation or Dilation).
1.
2.
3.
4.
7
5. Describe the translation using standard notation and
vector notation.
Standard: (x, y) → (x _______, y ________)
Vector: ⟨_____, _____⟩
6. Translate with the rule:
(x, y) → (x + 3, y – 2)
7. Translate with the rule:
(x, y) → (x – 1, y + 5)
Consider the translation that is defined by the coordinate notation (x, y)→(x – 3, y + 2).
8. What is the image of (2, 2)?
9. What is the image of (0, -2)?
10. Reflect the triangle in the x-axis
11. Reflect the triangle in the y-axis.
12. Reflect the figure over the line y = 1.
13. Reflect the figure over the line x = 2.
8
14. Rotate the figure 90
CCW. (x, y) → (-y, x)
15. Rotate the figure 180.
(x, y) → (-x, -y)
16. Rotate the figure 90
CCW. (x, y) → (y, -x)
The dashed triangle is a dilation image of the solid triangle. Decide if it is an enlargement or
reduction.
17.
18.
19.
Use the origin as the center of the dilation and the given scale factor to find the coordinates of the
vertices of the image of the polygon. Graph the new image.
20. k = 2
21. k = ½
22. k = 3
Find the scale factor for each dilation. Tell if it is a reduction or enlargement.
23.
24.
25.
9
Draw all lines of symmetry for the figures.
26.
27.
28.
29.
Does the figure have rotational symmetry? If so, what is the angle of rotation?
30.
31.
32.
33.
Chapter 5 Problems
1. Describe each type of triangle.
Right
Scalene
Acute
Isosceles
Obtuse
Equilateral
Equiangular
Classify each triangle by its angles and sides.
2.
3.
4.
5.
6.
7.
∆JKL  ∆MNO. Complete each statement.
8. J 
11. MO 
9. JK =
12. O 
10. mJ =
13. mO =
10
Find the value of the missing variables or value.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Are the triangles congruent? If yes, state the Postulate or Theorem you would use and mark any
side/angle congruencies you found and used to make your decision. (SSS, SAS, ASA, AAS, HL)
26.
27.
28.
11
29.
30.
32.
Given : CAB  DAB, C  D
Prove : ACB  ADB
31.
Statements
33.
Reasons
1. CAB  DAB, C  D
1.
2. AB  AB
2.
3. ACB  ADB
3.
Given : AB DC; AB  DC
Prove : ABE  CDE
Statements
Reasons
1. AB DC ; AB  DC
1.
2. A  C
2.
3. AEB  DEC
3.
4. ABE  CDE
4.
Chapter 6 Problems
1. Refer to the figure to the right.
A. LM//___________.
B. BC //___________.
C. If BC = 18, then
LN = _________.
D. If AB = 16, then
NM = __________.
2. Name the angles in ABC in
order from smallest to largest.
3. List the sides in JKL order
from shortest to longest.
12
Can you construct a triangle with the following side lengths?
4. 2, 3, 7
6. 4, 4, 4
5. 8, 8, 10
Two sides of a triangle are given. What is the possible length of the 3 rd side?
7.
2, 18
_______ < x < ________
8.
5, 12
_______ < x < ________
Chapter 7 Problems
1. State the name of each based on the number of sides.
2. Tell if the following is equilateral, equiangular, regular or none of these.
3. What is the sum of the measure of one interior angles of a heptagon?
Formulas:
Sum of Int. ’s: (n – 2)(180)
4. What is the measure of each interior angles of a regular octagon?
1 Int. :
5. What is the sum of the exterior angles of a decagon?
(n − 2)(180)
n
Sum of Exterior ’s: 360
6. How many sides does the figure have if one exterior angle is 60?
1 Ext. :
7. What is the measure of each exterior angle of a regular pentagon?
# of Sides:
360
n
360
Ext.
Find each measure.
8. m∠1
9. m∠A
10. m∠1
13
Decide if enough information is given to say that the quadrilateral is a parallelogram.
11.
12.
13.
14. Name each quadrilateral.
Find the missing values in each special quadrilateral.
15. Kite
16. Rhombus
mA =
m1 =
mT =
m2 =
m3 =
m4 =
17. Rectangle: m1 = 20
m1 = 20
m2 =
m3 =
m4 =
m5 =
m6 =
m7 =
m8 =
Find the missing angles in the isosceles trapezoids.
18.
19.
Solve for x.
20.
21.
14