Honors Geometry Name # 1st Semester Final Exam...

Honors Geometry Name_____________________________________#_______ 1st Semester Final Exam Review Chapter 1 Vocabulary and Theorems… (NOTE: All words have NOT been listed here)

Kite – A _______________ with __________________ pairs of _______________________sides.

Dart – A _______________ kite.

Trapezoid – A _______________ with _______________________ of _______ sides.

Isosceles Trapezoid – A _______________ with _______ legs.

Parallelogram – A _______________ with _______ pairs of _______________ sides.

Rhombus – An ______________________________ parallelogram.

Rectangle – An ______________________________ parallelogram.

Regular Polygon – A polygon that is _____________________ and _____________________.

Square – A ______________________________ parallelogram Chapter 2 Vocabulary, Theorems, and Formulas…

Linear Pair Postulate: If two angles form a ________________, then ________________.

Vertical Angles Theorem: If two angles are ________________, then _________________.

CA Postulate: If two lines are parallel, then ________________.

AIA Theorem: If two lines are parallel, then ________________.

AEA Theorem: If two lines are parallel, then ________________.

Converse CA Postulate: If ______________________, then ______________________.

Converse AIA Theorem: If ______________________, then ______________________.

Converse AEA Theorem: If ______________________, then ______________________.

Chapter 3 Vocabulary, Conjectures, and Formulas…

If a point is on the perpendicular bisector of a segment, then it is _______________________ from the

endpoints of the segment.

If a point is __________________ from the endpoints of a segment, then it is on the ________________

The shortest distance from a point to a line is measured along the _________________________ from

the point to the line.

If a point is on the bisector of angle, then it is _______________________ from the sides of the angle.

Remember: The distance from the point to the side must be measured on a _____________ line.

Point of concurrency for the angle bisectors in a triangle is called the _____________________ and can

be found in / out / on the triangle (Circle all that apply.)

Point of concurrency for the perpendicular bisectors in a triangle is called the _____________________ and can be found in / out / on the triangle (Circle all that apply.)

Point of concurrency for the altitudes in a triangle is called the _____________________ and can be found in / out / on the triangle (Circle all that apply.) The altitude is also called the ______________.

Point of concurrency for the medians in a triangle is called the _____________________ and can be found in / out / on the triangle (Circle all that apply.)

_____________________ is the center of gravity for the triangle.

_____________________ is equidistant from the sides of the triangle

and is used to ________________ a circle.

_____________________ is equidistant from the vertices of the triangle

and is used to _______________ a circle.

Note: The four points of concurrency will be the same in an ______________________ triangle.

The centroid of a triangle divides each median into two parts where… The distance from the centroid to the vertex is ______________ the distance from the centroid to the midpoint of the opposite side.

Chapter 4 Vocabulary, Theorems, and Formulas…

The sum of the measures of the angles in every triangle is _______________.

If a triangle is isosceles, then ______________________________________________.

If a triangle has two congruent angles, then ______________________________________________.

The sum of the lengths of any two sides of a triangle is _________ than the third side

Does it make a triangle? Fast check______________________________________________________

In a triangle, if one side is longer than another side, then the angle opposite the longer side is

____________________________________________________________________________________

The measure of an exterior angle of a triangle is …

____________________________________________________________________________________

If three sides in one triangle are congruent to three sides of another triangle, then __________________.

If two sides and the included angle of one triangle are congruent to two sides and the included angle of

another triangle, then __________________.

If two angles and the included side of one triangle are congruent to two angles and the included side of

another triangle, then __________________.

If two angles and a non-included side of one triangle are congruent to two angles and a non-included

side of another triangle, then __________________.

Note: What patterns CANNOT be used to prove that two triangles are congruent? _______ & _______

In an isosceles triangle, the bisector of the __________________is also the …

__________________, __________________ and the __________________ to the base

Every equilateral triangle is_______________________________.

Every equiangular triangle is _______________________________. Chapter 5 Vocabulary, Conjectures, and Formulas…

POLYGONS…

The sum of the measures of the n interior angles of an n-gon is _______________.

For any polygon, the sum of the measure of a set of exterior angles is _______________.

You can find the measure of each interior angle of an equiangular n-gon by using either of these

formulas: _______________(symbols) or _______________(words). KITES…

The ____________________ angles of a kite are _______________.

The diagonal connecting the ____________________ angles of a kite is the _________________ of the

other diagonal.

The ____________________ angles of a kite are _______________ by the diagonal. TRAPEZOIDS…

The ____________________ angles between the bases of a trapezoid are _______________.

Each pair of _______________ angles in an isosceles trapezoid are ____________________.

The __________________ in an isosceles trapezoid are ____________________.

MIDSEGMENTS…

The ____________ midsegments of triangle divide the triangle into____________________________.

A midsegment of a triangle is ________________ to the ________________ side.

A midsegment of a triangle is ________________ the length of the ________________ side.

A midsegment of a trapezoid is ________________ to the ________________.

A midsegment of a trapezoid is ________________ of the lengths of the ________________. PARALLELOGRAMS…

The ____________________ angles in a parallelogram are ____________________________.

The ____________________ angles in a parallelogram are ____________________________.

The ____________________ sides in a parallelogram are ____________________________.

The ____________________ sides in a parallelogram are ____________________________.

The ____________________ in a parallelogram ____________________________.

RHOMBI…

The diagonals of a rhombus are_________________________ to each other.

The diagonals of a rhombus __________________ each other.

The _______________________ of a rhombus _________________________ the angles

RECTANGLES…

The diagonals of a rectangle are ____________________ and ____________________ each other. SQUARES…

The diagonals of a square are ________ , and ____________, and they ________________ each other.

Chapter 6 Vocabulary, Conjectures, and Formulas…

A tangent to a circle _________________ to the radius at the point of tangency

Tangent segments to a circle from a point outside the circle are _________________

Circles are considered internally or externally tangent when they are _________________ to the same

_____________ at the same ______________.

The measure of the central angle is the _____________ arc

If two chords in a circle are congruent, then they determine _________________ angles.

If two chords in a circle are congruent, then their _________________ are congruent

The perpendicular from the center of a circle to a chord is the _________________ of the chord.

Two congruent chords in a circle are _________________ from the center of the circle.

The measure of an angle inscribed in a circle is… _______________________________________.

Inscribed angles that intercept the same arc… _______________________________________.

Angles inscribed in a semicircle… _____________________________________.

The _______________ angles of cyclic quadrilateral are ________________________.

Parallel lines intercept _____________________ on the circle.

The measure of an angle formed by 2 secants that intersect outside the circle is ___________________

The measure of angle formed by 2 intersecting chords is ___________________

The measure of an angle formed by an intersecting tangent and a secant to a circle is ______________

The measure of angle formed by 2 intersecting tangents to a circle is ___________________

The measure of an angle formed by the intersection of a tangent and a chord at the point of tangency is

___________________

The formula for the area of a circle is ________________________________

The formula for the circumference of a circle is ________________________________

The formula for arc length is ________________________________

Apply what you know…

1. Ch 3 Do you remember your constructions? p.160: 1-5... p.184: 22-24… p.194: 11-18

2. How do you know if two statements are equivalent?

3. The conditional statement and the ____________________________ are equivalent statements.

4. The inverse and the ____________________________ are equivalent statements.

5 For a biconditional statement to be true, the ______________________ and ______________________

must both be ______________.

6. Given the following statement: If it is Thanksgiving, then it is Thursday…

Write the inverse and contrapostive.

7. Given the following statement: If one light on the strand is broken, then the strand won’t work. …

Write the inverse and converse.

8. Write the following in if-then form: Ms. Bass tutors at Barnes and Noble if it is Tuesday.

9. Determine if the following biconditional is true…

A quadrilateral is a rhombus if and only if it an equilateral parallelogram. 10. Given the following statement: If polygon is a kite, then it does not have a pair of parallel sides …

Write the converse and contrapostive. 11. Write the converse of the following statement AND give a counterexample to prove it’s false…

If an angle is inscribed in a circle, then its measure is one-half of the intercepted arc.

Use the diagram below and the given information to identify the type of angle pair (IF ANY) and solve for x.

12. What kind of angle pair is 2 and 3?

If m // n , 2 3 12m x , and 3 4 7m x .


If m // n , 7 16 20m x , and 5 13 7m x

.


If m // n , 8 6m x , and 7 13 10m x


If m // n , 1 4 5m x , and 5 3 11m x


If m // n , 2 7 12m x , and 4 3m x


If m // n , 81 8 40m x and 5 6m x


If m // n , 1 3 18m x , and 6 108m

1

8

7

2

3 m

4 n

5 6

19. Find slope of the line through the points

6, 12 and 24, 12

20. Write the equation (in slope-intercept) of the

line passing through 5, 4 and 10, 26

21. Determine if the measures can form the

sides of a triangle.

a. 70, 79, 18

b. 72, 5, 77 c. 14, 90, 25

22. Given 2 sides of triangle, between what 2 numbers must the measure of 3rd side fall.

a. 37 and 16

b. 5 and 23 c. 41 and 28

23. In ΔCAT, 7 10m C x ,

3 14m A x , and 6 20m T x ,

determine the order the SIDES from longest

to shortest.

24. What is the longest side in the figure.

25. What is the longest side in the figure.

26. In ABC, BCAB , and 90m B and

4 1m A x . Solve for x.

27. In DEF, 60m E m F ,

7 2DF x , and the perimeter of DEF

51 cm. Solve for x.

28. In isosceles triangle GHI, I is the vertex

angle and 72m G . Find m I

29. In the figure below, 7 9m ABD x

6m D x , and 42 2m C x .

Solve for x.

30. Find the sum of the interior angles of a

convex 35-gon.

A. 5940

B. 6300

C. 6660

D. 11880

31. If the measure of an exterior angle of a

regular convex polygon is 1.2, find the number of sides in the polygon.

A. 50

B. 75 C. 150

D. 300

32. Find the measure of an interior angle of a

regular undecagon.

A. 140

B. 147.27

C. 150

D. 163.64

33. If the sum of the interior angles of a regular

polygon is 2700, find the measure of each interior angle.

A. 152.31

B. 156

C. 158.82

D. 168

34. Determine which of the following is a parallelogram.

a.) b.)

c.) d.)

89 A 82

25

43 L

73 F 48

T

34 R 60

56

76 I

T E 64 70

B C

D

A

R

C

D

36°

35. Solve for x… ABCD is a parallelogram.

13 27m B x , 49m C .

A. 1.08 B. 1.69

C. 8

D. 21.85

36. If EFGH is a parallelogram, complete each

statement.

a.) FEH ______________

b.) FG = _________________

c.) FJ = __________________

d.) HEG ______________

e.) m GFE ______________ = 180

37. Solve for x.

A. 64

B. 73

C. 128

D. 67

E. None of these

38. Solve for x.

A. 15

B. 14

C. 43

D. 29

E. None of these

39. If mA = 88 and mAC = 80. Find mC.

A. 52

B. 12

C. 104

D. 116

E. None of these

40. A , mCD = 162, 51m A

Find mCE .

A. 147

B. 35.96

C. 213

D. 96

E. None of these

41. mADC = 204, mBC = 93. Find mACB.

A. 63

B. 297

C. 31.5

D. 126

E. None of these

42. The radius of the circle is 25 cm. Find CD .

43. Given T where 90mAB and

12AB cm , find the length of the radius

of T .

61º 67º xº

B

A

C

C

A

D E

A

B

D

C

190º

xº

58º 84º

F G

J

E H

Answer the following with always, sometimes, or never.

44. A parallelogram is ________________ a quadrilateral.

45. A kite is __________________ a rectangle.

46. A rhombus is _________________ a square.

47. A parallelogram is ___________________ a trapezoid.

48. A trapezoid is ____________ a quadrilateral.

49. The diagonals of a parallelogram are _____________ equal.

50. The diagonals of a rectangle are _______________perpendicular.

51. The diagonals of a rhombus are _______________ equal.

52. Trapezoids are _______________kites.

53. The angles of are rhombus are _______________ right angles.

54. Parallelograms are _____________squares.

Write 2 column proof for each of the following.

55. Given: C is the midpoint of BE

B E

Prove: DBC AEC

56. Given: BD is a perpendicular bisector of AC

Prove: ABC is isosceles with vertex B

57. WRITE AN INDIRECT PROOF…

Given: BD is not AC

BD bisects ABC

Prove: A is not C

A

B

C

D

E

A C D

B

A C D

B

EXTRA REVIEW…

1-26… Identify each statement as true or false.

1. Every rhombus is a square.

2. The complement of an acute angle is another acute angle

3. Any point on the perpendicular bisector of a segment is equally distant from the two endpoints of the

segment.

4. The centroid of a triangle is the point of concurrency of the three medians in the triangle

5. The midsegment of a trapezoid is equal in length to the average of the two base lengths.

6. The measure of each exterior angle of a regular octagon is 45.

7. In a triangle, the angle with the least measure is opposite the longest side.

8. Two shortcuts for showing two triangles are congruent are ASA and SSA.

9. The diagonals of a kite are perpendicular bisectors of each other.

10. The angle bisector in a triangle bisects the opposite side.

11. Any point on the angle bisector of an angle is equally distant from the two sides of the angle.

12. If point A has coordinates (0, 3) and point B has coordinates (8, -5), then the midpoint of AB is found

at (4, 4).

13. Given two sides and an included angle, exactly one triangle can be constructed.

14. The sum of the measures of any two consecutive angles of a parallelogram is 180.

15. If the diagonals of a quadrilateral are perpendicular, then the quadrilateral must be a square.

16. If the diagonals of a quadrilateral are congruent, then the quadrilateral must be a rectangle or

square.

17. Making a conjecture from your observations is called deductive reasoning.

18. In a linear pair of angles, one of the angles must be obtuse.

19. A trapezoid has exactly one pair of congruent sides.

20. A scalene triangle has no sides of the same length.

21. A square is both a rhombus and a rectangle.

22. ABC has vertex C.

23. If two lines are cut by a transversal to form a pair of congruent corresponding angles, then

the lines are parallel.

24. When you construct a figure, you use only a compass and a protractor.

25. The incenter of a triangle is the intersection of the perpendicular bisectors of its sides.

26. It is possible to create a triangle with side lengths 12 cm, 7 cm, and 5 cm.

27 – 37… Fill in the blank.

27. If 1 and 2 form a linear pair and m 1 = 64°, then .

28. Each point on the of a segment is equidistant from the endpoints of the segment.

29. In a regular pentagon, each interior angle has measure _____________.

30. If one of the base angles of an isosceles triangle has measure 40°, then the vertex angle has

measure ________________.

31. In ABC, if mA = 50°, mB = 72°, and mC = 58°, then ________________ is the

longest side.

32. In a regular n-gon, each exterior angle has measure _______________.

33. If the midsegment of a trapezoid has length 6 cm, and one of the bases has length 4 cm, then

the other base has length ________________.

34. The two diagonals of a ________________ are perpendicular bisectors of one another, are

congruent, and bisect the angles.

35. What is the sum of the measure of the interior angles of a dodecagon?

36. Which point of concurrency is equidistant from the three vertices of a triangle?

37. Which point of concurrency is equidistant from the three sides of a triangle?

Use the figure at the right for #38 and #39

38. If AD || BC and CD AB …

Is ∆ABD ∆CDB? Why or why not?

39. If AD || BC and AD BC …

Is ∆ABD ∆CDB? Why or why not?

40. If ∆ CAT ∆ DOG, which of the following is not necessarily true?

A. ATC DGO

B. CT DG

C. AT DO

D. CAT DOG

E. CA DO

41. Which of the following polygons will not necessarily have any congruent interior angles?

A. Equilateral triangle

B. Square

C. Trapezoid D. Regular pentagon

E. Rectangle

D C A B

46. Give an example of each of the following segments in ΔABC.

a.) a median

b.) a perpendicular bisector

c.) an altitude

d.) an angle bisector

e.) a midsegment ________

49. Find the measures of the lettered angles.

50. Find the measures of the lettered angles.

C B

A

D

F G

46º 46º

E

Additional Answers… Apply what you know

6. Inverse

If it is not Thanksgiving, then it is not Thursday.

Contrapositive If it not Thursday, then it is not Thanksgiving.

7. Inverse

If one light on the strand is not broken, then the strand will work.

Converse If the strand won’t work, then one like on the strand is broken.

8. If it is Tuesday, then Ms. Bass tutors at Barnes and Noble.

9. Conditional If a quadrilateral is a rhombus, then it is an equilateral parallelogram.

Converse If a quadrilateral is an equilateral parallelogram, then it is a rhombus.

Both are true so the biconditional is true.

10. Converse

If a polygon does not have a pair of parallel sides, then it is a kite. Contrapostive If a polygon has a pair of parallel side, then it is not a kite.

11. Converse

If an angle’s measure is one-half its intercepted arc, then the angle is inscribed in a circle. Contrapositive False!

The measure of this angle is

one-half its intercepted arc,

but it’s not an inscribed angle.

Proof solutions are on the next page…

Proofs… These are how I completed the proofs. Remember, there are usually multiple ways to complete a proof and some steps can be rearranged. Please see me if you are unsure if your solutions is correct.

55.

1. C is the midpoint of BE 1. Given

2. BC EC 2. Defn midpoint

3. B E 3. Given

4. &CDB ECA are VA 4. Def VA

5. CDB ECA 5. VA Theorem

6. DBC EAC 6. ASA

56.

1. BD is perpendicular bisector of AC 1. Given

2. D is the midpoint of AC 2. Def Perp Bisector

3. AD CD 3. Defn midpoint

4. BD AC 4. Def Perp Bisector

5. &BDA BDC are right angles 5. Def Perp Lines

6. BDA BDC 6. All right angles congruent

7. BD BD 7. Reflexive

8. DBC EAC 8. SAS

9. AB CB 9. CPCTC

10. ABC is isosceles w vertex B 10. Defn isosceles triangle

57. 1. Assume A C 1. Opposite of prove

2. AB BC 2. Converse Isos Triangle Thm

3. ABC is isosceles w vertex B 3. Defn isosceles triangle

4. BD bisects ABC 4. Given

5. BD is an altitude 5. Vertex angle in isos bisected altitude

6. BD AC 6. Defn Altitude

7. But BD is not AC 7. Given

8. A is not C 8. Contradiction

Honors Geometry Name # 1st Semester Final Exam...

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