Download geometry – first semester exam review

GEOMETRY – FIRST SEMESTER EXAM REVIEW
VOCABULARY: You need to know (and understand) the formal definitions of these terms. You will
need to know them to answer multiple choice questions and solve problems on the written part of the test.
1.
2.
3.
4.
5.
6.
7.
Equilateral Triangle
Equiangular Triangle
Acute Triangle
Scalene Triangle
Obtuse Triangle
Right Triangle
Isosceles Triangle
8. Perpendicular Bisector
9. Angle Bisector
10. Median
11. Altitude of a Triangle
12. Centroid
13. Circumcenter
14. Incenter
15. Orthocenter
16. Parallelogram
17. Rectangle
18. Rhombus
19. Square
20. Trapezoid
21. Isosceles Trapezoid
22. Vertical Angles
23. Linear Pair
24. Alternate Interior Angles
25. Corresponding Angles
26. Consecutive Interior Angles
27. Alternate Exterior Angles
28. Conditional Statement
29. Converse
30. Inverse
31. Contrapositive
32. Hypothesis of a conditional
33. Conclusion of a conditional
34. Complementary Angles
35. Supplementary Angles
36. Regular Polygon
37. Parallel Lines
38. Skew Lines
39. Parallel Planes
FORMULAS – These are formulas you should have memorized and be able to use on the exam when
necessary.
1. Distance
2. Midpoint
3. Slope
4. Sum of the measures of the interior angles of a polygon
5. Measure of each interior angle of a regular polygon
6. Sum of the measures of the exterior angles of a polygon
7. Measure of each exterior angle of a regular polygon
POSTULATES, PROPERTIES AND THEOREMS
1. All the postulates from section 2-5 (page 127) – Used for sometimes/always never
2. All the properties from section 2-6 (page 136)
3. Segment Addition Postulate
4. Angle Addition Postulate
5. Vertical Angle Theorem
6. Corresponding Angle Postulate
7. Alternate Interior Angle Theorem
8. Consecutive Interior Angle Theorem
9. Alternate Exterior Angle Theorem
10. Triangle-Angle Sum Theorem
11. Exterior Angle Theorem
12. SSS
13. SAS
14. ASA
15. AAS
16. Perpendicular Bisector Theorem
17. Circumcenter Theorem
18. Angle Bisector Theorem
19. Incenter Theorem
20. Centroid Theorem
21. Reminder to study the chart on page 339!!!
22. Exterior Angle Inequality Theorem
23. Angle-Side Relationships in Triangles (pg 346)
24. Triangle Inequality Theorem
25. Hinge Theorem
26. Properties of Parallelograms (pg 403-405)
27. Properties of Rectangles (pg 423)
28. Properties of a Rhombus (pg 430)
29. Properties of a Square
30. Properties of Trapezoids and Isosceles Trapezoids
PRACTICE PROBLEMS – The rest of this review is made up of practice problems similar to what you
will see on the exam in either the multiple choice or the written portion.
1.
Classify the following pairs of angles using the diagram below. Remember that “none” is an
option.
a.  9 and  13 _______________________
b.  1 and  11 _______________________
c.  5 and  6 _______________________
d.  3 and  13 _______________________
e.  7 and  13 _______________________
f.  3 and  8 _______________________
g.  1 and  3 _______________________
2.
Use the diagram to the right to determine which lines, if any, must be parallel given the information below.
a.  10 =  2 _________________________
b.  11 =  13 __________________________
c.  5 +  12 =180 _________________________
d.  1 =  3 _______________________________
3.
Write the converse, inverse and contrapositive of the following statement:
If two angles are supplementary, then their measures add to 180 degrees
a.
Converse: __________________________________________________________________
b.
Inverse: ____________________________________________________________________
c. Contrapositive: _______________________________________________________________
4.
Use the statement below to identify the hypothesis and the conclusion:
If 2x – 5 = 11, then x = 8
Hypothesis: _______________________________
Conclusion: _______________________________
5.
List what postulate or theorem could be used to prove the triangles congruent and then write the
congruence statement.
a.
b.
_________________
________________
_________________
_________________
6.
Find the sum of the measures of the interior angles of a convex 22-gon.
7.
Find the sum of the measures of the exterior angles of a decagon.
8.
Find the distance between the two points A (-3, -7) and B (4, 3).
9.
Find the midpoint of a segment with the endpoints X(10, -4) and Y(-3, 9).
For 10-11 use the figure at the right.
⃗⃗⃗⃗ .
10. If m  RTS = 8x + 18, find the value of x so that ⃗⃗⃗⃗⃗
TR  TS
11. If m  PTQ = 3y –10 and m  QTR = y, find the value of y so that
 PTR is a right angle.
12.
Construct a truth table for the statement (4 points)
~p v (q ᴧ r)
For 13-15, find the measure of each numbered angle using the diagrams and information below.
13.
14.
m∠7 = 5x + 5,
m∠8 = x – 5
15.
∠9 and ∠10 are complementary
∠7 ≅ ∠9, m∠8 = 41
m∠11 = 11x,
m∠13 = 10x + 12
16. Find X and Y.
X: ___________________
Y: ___________________
17. In the diagram below m  2 = 96 and m  12 = 103. Find the measures of the angles below.
a.
 9 ____________
b.
 10 _____________
c.
 5 ______________
d.
 11 _____________
e.
 13 ______________
f.
 8 _______________
For 18 and 19, write the equation of each line in slope-intercept form with the given information.
18.
m=-
3
and through point (-4, 6)
2
19.
Through points (-4, 2) and (8, -1)
For 20 and 21, use the diagram to classify the given triangles by SIDES.
20.
21.
For 22 and 23, use the diagram to classify the triangles by ANGLES.
22. XUZ ______________
23. UYX __________________
24.
In △MIV, Z is the centroid, MZ = 4, YI = 21, and NZ = 3. Find each measure.
A) ZR __________
B) YZ __________
C) MR __________
D) ZV __________
E) NV __________
F) IZ __________
25.
Point A is the incenter of △PQR. Find each measure.
A) m  ARU _______________
B) AU _______________
C) m  QPK _______________
26.
Is it possible to form a triangle with side lengths of 12, 13, 14? If not, explain why not.
27.
Is it possible to form a triangle with side lengths of 20, 43, 22? If not, explain why not.
28.
Find the range of the measures of the third side of the triangle given that the other two sides are
32cm and 150cm.
For 29 and 30, use an inequality to compare the given measures.
29. m∠ STR and m∠ TRU
_________________
30.
PQ and RQ
________________
For 31 and 32 use RECTANGLE RSTU. Circle your answer.
31.
If UZ = 3x - 5 and ZS = 2x + 11, find US.
32.
If m∠SUT = 2x - 7 and m∠RUS = 2x + 5, find m∠SUT.
For 33-35, use RHOMBUS DKLM. Circle your answer.
33. If m∠DML = 78 find m∠DKM.
34.
If m∠KAL = 3x - 15, find x.
35.
If DA = 3x - 1 and AL = x + 9, find DL.
PROOF REVIEW
Do all your proofs on a separate sheet of paper. These should be two-column proofs
1.
Given:
4𝑥 + 6
2
=9
Prove: x = 3
2.
Given: −5(𝑥 + 4) = 70
Prove: x = -18
3.
Given: 1  4 AND 2  3
Prove:  AFC =  EFC
4.
Given: X is the midpoint of WY and VZ
Prove: VW = ZY
5.
Given: m∠1 + m∠3 = 180
Prove: ∠2 ≅ ∠3
6.
Given: AB = DE and BC = EF
Prove: AC = DF
7.
8.
Given: 𝑟 ∥ 𝑠
Prove:∠1 is supplementary to ∠6
9.
Given: ∠1 ≅ ∠2, ∠1 ≅ ∠3
̅̅̅̅ ∥ ̅̅̅̅
Prove: 𝑨𝑩
𝑫𝑪
10.
11.
Given: ∠S ≅ ∠V,
T is the midpoint of ̅̅̅̅
𝑆𝑉.
Prove: △RTS ≅ △UTV
12.
13.
Given: ∠D ≅ ∠F
̅̅̅̅
𝐺𝐸 bisects ∠DEF.
Prove: ̅̅̅̅
𝐷𝐺 ≅ ̅̅̅̅
𝐹𝐺
14.
15.
For 16 and 17, write an INDIRECT PROOF. Makes sure to include all the steps of an indirect proof.
16.
Given: -4x + 2 < -10
Prove: x > 3
17.
Given: 5x – 2 < 13
Prove: x < 3