Download HGeo T! Prac Final

Name: ______________________
Class: _________________
Date: _________
ID: A
Honors Geometry Term 1 Practice Final
Short Answer
5. Line p 1 has equation y = −3x + 5. Write an
equation of line p 2 which is perpendicular to p 1
and passes through the point ÊÁË −3, 6 ˆ˜¯ .
1. RT has endpoints R ÊÁË −4, 2 ˆ˜¯ , T ÊÁË 8, − 3 ˆ˜¯ . Find the
coordinates of the midpoint, S, of RT.
2. If m∠3 = 68 û , find the measures of ∠5 and ∠4.
6. In ΔABC, the measure of ∠A = 116 û . The
measure of ∠B is three times the measure of ∠C.
Find m∠B and m∠C.
3. If l Ä m, which angles are supplementary to ∠1?
Decide whether it is possible to prove that
the triangles are congruent. If it is possible,
tell which congruence postulate or theorem
you would use. Explain your reasoning.
7.
Decide whether lines p 1 and p 2 are
perpendicular.
4.
8.
1
ID: Version
9.
15.
10.
16.
11.
17.
12.
18.
13.
19.
14.
2
ID: Version
Find the value of x.
Use the diagram.
20.
24. Point H is the ? of the triangle.
21.
25. CG is a(n) ? , ? , ? , and ?
22.
26. EF =
? and EF Ä ? by the ?
of ΔABC.
Theorem.
27. The vertices of ΔPQR are P ÊÁË −2, 3 ˆ˜¯ , Q ÊÁË 3, 1 ˆ˜¯ , and
R ÊÁË 0, − 3 ˆ˜¯ . Decide whether ΔPQR is right, acute,
or obtuse.
23.
28. Q is between P and R.
PQ = 2w − 3, QR = 4 + w, PR = 34. Find the value
of w. Then find the lengths of PQ and QR.
29. Suppose m∠PQR = 130 û . If QT bisects ∠PQR,
what is the measure of ∠PQT?
3
ID: Version
30. A tool and die company produces a part that is to
be packed in triangular boxes. To maximize space
and minimize cost, the boxes need to be designed
to fit together in shipping cartons. If ∠1 and ∠2
have to be complementary, ∠3 and ∠4 have to
be complementary, and m∠2 = m∠3, describe the
relationship between ∠1 and ∠4.
Write an equation of the line described.
34. The line that is parallel to the line with equation
y = −2x + 3 and passes through the point
ÊÁ −1, − 2 ˆ˜ .
Ë
¯
35. The line that is perpendicular to the line with
equation y = −2x + 3 and passes through the point
ÁÊË −2, − 1 ˜ˆ¯ .
Use the diagram to find the measure of the
given angle.
Identify all triangles in the figure that fit
the given description.
36. isosceles
31. m∠1 = 75 û . Find m∠2.
37. acute
Use the diagram to find the measure of the
given angle.
38. Find the perimeter of ΔBCD.
32. m∠1 = 75 û . Find m∠5.
33. m∠1 = 75 û . Find m∠8.
4
ID: Version
Use the diagram. Find the length of the
segment.
44.
45.
39. HC
40. HB
Use the figure to complete the statement.
41. HE
42. EF
46. ∠2 and ∠7 are ? angles.
Name the special segments and the point of
concurrency of the triangle.
47.
∠4 and ∠5 are ? angles.
43.
Find the value of x.
48.
5
ID: Version
Determine whether it is possible to draw a
triangle with sides of the given lengths.
Write yes or no. If yes, determone the type
of trinagle it is: acute, right or obtuse and
scalene, isosceles or equilateral.
49.
54. 3, 4, 5
55. 4.7, 9, 4.1
50.
56. 4, 9, 13
Use the triangle below. The midpoints of the
sides of ΔABC are F, E, and D.
51.
52.
57. FD ≅ __________?
58. If DE = 10, then AB = __________ ?
53.
59. If the perimeter of ΔFDE is 18, then the
perimeter of ΔABC is _______?
6
ID: Version
List the sides in order from shortest to
longest.
Complete the statement with the word
inside, on, or outside.
60.
64. In an acute triangle, the altitudes intersect
the triangle.
65. In a right triangle, the altitudes intersect
the triangle.
66. In an obtuse triangle, the altitudes intersect
the triangle.
61.
Complete the statement with the word
always, sometimes, or never.
67. The perpendicular bisectors of a right triangle
will
intersect outside the
figure.
62.
68. The medians of an obtuse triangle will
intersect inside the triangle.
69. The perpendicular bisectors of an obtuse triangle
will
intersect on the triangle.
63. In ΔXYZ and ΔRST, which is longer, XZ or RT?
70. The midsegment of a triangle will
parallel to two sides of the triangle.
7
be
ID: Version
Complete the statement by writing
< , = , or >.
71. m∠ADC
72. AB
73. m∠1
m∠2
74. m∠5
m∠6
m∠ADB
AC
8
ID: Version
Other
Complete the proof.
Write a two-column proof.
75. Given: ∠ABC ≅ ∠ABD, ∠ACB ≅ ∠ADB
76.
Given: BD ≅ EC, AC ≅ AD
Prove: ΔACB ≅ ΔADB
Prove: AB ≅ AE
Statements
Reasons
1. ∠ABC ≅ ∠ABD
1. __________________
2. ∠ACB ≅ ∠ADB
2. __________________
3. AB ≅ AB
3. __________________
4. ΔACB ≅ ΔADB
4. __________________
9
ID: Version
77. Write a two-column proof.
Given: SR bisects ∠TSQ, ∠T ≅ ∠Q
Prove: ΔRTS ≅ ΔRQS
10
ID: A
Honors Geometry Term 1 Practice Final
Answer Section
SHORT ANSWER
1.
2.
3.
4.
S(2, 0.5)
m∠5 = 68 û ;m∠4 = 112 û
∠2, ∠4, ∠6, ∠8
yes
1
5. y = x + 7
3
6. m∠C = 16 û , m∠B = 48 û
7. Yes; ASA Congruence Postulate. Since ∠LMP ≅ ∠NPM and ∠NMP ≅ ∠LPM (given), and MP ≅ MP (reflexive
property of congruence), two pairs of corresponding angles are congruent and two corresponding included
sides are congruent.
8. no
9. yes; HL Theorem
10. yes; SAS
11. no
12. yes; ASA
13. yes; SSS
14. No; only one common side and one set of corresponding angles are congruent.
15. Yes; SAS, reflexive property, two pairs of corresponding sides and the included angles are congruent.
16. Yes; SSS, reflexive property and three pairs of corresponding sides are congruent.
17. Yes; AAS, vertical angles are congruent, one other pair of corresponding angles and one pair of corresponding
sides are congruent.
18. No; only two pairs of corresponding angles are congruent.
19. Yes; SAS, two pairs of corresponding sides and the angles included are congruent.
20. x = 7
21. x = 22.5
22. x = 55
23. x = 5
24. centroid
25. median, perpendicular bisector, angle bisector, altitude
1
26. EF = AB, EF Ä AB by the Midsegment Theorem.
2
27. acute
28. w = 11; PQ = 19; QR = 15
29.
30.
31.
32.
33.
m∠PQT = 65 û
∠1 ≅ ∠4 by the Congruent Complements Theorem
m∠2 = 105 û
m∠5 = 75 û
m∠8 = 75 û
1
ID: A
34. y = −2x − 4
1
35. y = x
2
36. ΔQPS and ΔQSR
37. ΔQPS
38. 64
39. 12
40. 10
41. 5
42. 8
43. angle bisectors; incenter
44. perpendicular bisectors; circumcenter
45. medians; centroid
46. alternate exterior angles
47. alternate interior angles
48. 13
49. 21
50. 1
51. 20
52. 45
53. 78
54. yes
55. no
56. no
57. BE and CE
58. 20
59. 36
60. QR, RS, QS
61. AC, CB, AB
62. RS, RT, ST
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
RT
inside
on
outside
never
always
never
never
<
>
>
<
2
ID: A
OTHER
75.
76.
Statements
Reasons
1. ∠ABC ≅ ∠ABD
1. Given
2. ∠ACB ≅ ∠ADB
2. Given
3. AB ≅ AB
3. Reflexive property
4. ΔACB ≅ ΔADB
4. AAST heorem
Statements
Reasons
1. BD ≅ EC, AC ≅ AD
1. Given
2. ∠1 ≅ ∠2
2. Base angles of an isoceles triangle
are congruent.
3.
ABD ≅
AEC
4. AB ≅ AE
3. SASCongruence Postulate
4. Corresponding parts of congruent
triangles are congruent.
77.
Statements
Reasons
1. SR bisects ∠TSQ
1. Given
2. ∠1 ≅ ∠2
2. Def. of angle bisector
3. ∠T ≅ ∠Q
3. Given
4. RS ≅ RS
4. Reflexive prop. of congruence
5. ΔRTS ≅ ΔRQS
5. AASCongruence Post.
3