Download Fall Review-Geometry PAP 1) Find the values of x and y. 2) bisects

Fall Review-Geometry PAP
1) Find the values of x and y.
2)
bisects
3) If
congruence?
and
measures
and
°. Find the measure of
, then
.
. This illustrates which property of
Use the diagram to decide whether the congruence statement below the picture is true.
Explain your reasoning.
4)
5) True or False: Vertical angles are always supplementary.
6) True or False: If two angles are supplements of the same angle, then they must be equal in
measure.
7) Find AB and BC in the situation shown at right.
AB = x + 16, BC = 5x + 10, AC = 56
8) Let
be between
=
and . Use the Segment Addition Postulate to solve for CD.
=
w = 24
9) What is the slope of a line parallel to the line
10) In the diagram, X is the incenter of
. Find x.
?
11)
are supplementary angles.
are vertical angles. If
what is
12) Write all possible names for the angle to the right.
13) Given:
is the perpendicular bisector of
. Name three things that you can conclude.
14) The medians of a triangle are concurrent. Their common point is the ____.
15) Given that a || b, what is the value of x? (The figure may not be drawn to scale.)
16) Use the figure to find the measure of
Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?
17
18
19
20) Find the measures of all three angles of the triangle.
For #21-26, find the value of x.
21
24
22
25
23
26
27) Two sides of a triangle have lengths 14 and 10. What are the possible lengths of the third
side x?
28) Which is the appropriate symbol to place in the blank? (not drawn to scale)
AB __ AC
29) Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither.
Line 1 passes through (10, 7) and (13, 9)
Line 2 passes through (–4, 3) and (–1, 5)
30) Given:
and
. What other piece of information is needed to show
by ASA Congruence Postulate?
31)Find the measure of exterior angle A.
33)
32) Find the measures of angles A,
B, and C.
is an altitude of PQR. Therefore, PQR is ______.
34) In
,
. The length of
is four times the length of . Find the lengths of all
three sides of the triangle if the perimeter of the triangle is 63 inches.
35) If
36) In
is the perpendicular bisector of
, then KGF
, AB = 3x – 2, BC = x + 4, and AC = 7. Also
______.
. Classify the triangle.
37) Identify the congruent triangles. How do you know they are congruent?
38) Can you use the SAS Congruence Postulate to prove that the two triangles are congruent?
Explain your reasoning.
39) A dirt path connects the lanes of a divided highway that runs east-west. An officer in a police car headed east gets a call that requires crossing over to the westbound lanes using the dirt
path.
Through what angle must the police car turn at the bend in the dirt path?
40) Write the slope-intercept form of the equation of the line passing through the point (5, –4)
and perpendicular to the line
41) Using the Triangle Inequality Theorem, solve for all possible values of x.
42) Two sides of a triangle have lengths 7 and 13. The third side has a length that is ______.
43) Solve for x.
44) The two triangle-shaped gardens are congruent. Find the missing side lengths and angle
measures.
45) A triangle has angle measures of 60°, 60°, and 60°. Choose the term that describes the triangle.
F Equiangular
G Right
H Obtuse
J Scalene
46) Refer to the figure at right.
.
47) For the cube shown, name all lines that are skew to
48) Refer to the figure at right.
If EF = 5x + 6 and AC = 3x – 2, then what is the length of
.
?
49) If ABC
DEF, AB = 6 feet, m B = 55°, and m F = 69°, which of the following
statements is false?
F
G
H
56°
J
50) Solve for x given
=
and
Assume B is the midpoint of
=
.
and D is the midpoint of
51) Find the length of
52) Line m is parallel to line n and they are each intersected by the same two transversals.
Which angle is NOT necessarily congruent to
53) Solve for x, given that
54) Find the value of x.
. Is
equilateral?
55) Find AB and BC in the situation shown below.
BC = 7x – 13, AB = 4x + 26, B is the midpoint of
.
56) Refer to the figure
below. What can
be concluded?
57) Find the value of z. Is there enough information to show that D lies on the vertical line
that passes through B?
58) Identify the congruent triangles. How do you know they are congruent?
59) The following measures represent the acute angles of a right triangle. Find the measure of
each angle.
60) Write the converse of the true statement and decide whether the converse is true or false. If
the converse is true, combine it with the original statement to form a true biconditional statement. If the converse is false, state a counterexample:
If two lines are parallel, then they never intersect.
61) Using the Triangle Inequality Theorem, solve for all possible values of x.
62) Which best describes the relationship between Line 1 and Line 2?
Line 1 passes through
and
Line 2 passes through
and
63) Find m 1 in the figure below.
64) You know that
bisects
and
are parallel.
BAC, and that m CAD is 45°.
a. Draw a sketch that shows that
bisects BAC.
b. Find the measure of BAC. Explain how you found your answer.
65) Find the distance between the lines with the equations
66) The midpoints of the sides of a triangle are
ordinates of the vertices?
67) Write the equation of the line that is parallel to
point (6, 2).
68)
form a linear pair. If
, what is
69) Find the distance between the points (–7, 3) and (–15, –3)
70) Find the midpoint between (-2, 7) and (6, -1).
and
and
.
What are the co-
and passes through the
71) Determine if the triangles are similar. If they are, give the reason.
40
35
35
40
72) Determine if the triangles are similar. If they are, give the reason.
8
6
12
9
73) Using the figure to the right, complete the following:
m<C = _________
R
QT = __________
9
100
Scale factor: ________________
B
S
3
C
6
4
60
Q
A
T
8
D
A
B
74) Using the figure to the right, find the length of FG.
12
10
C
5
G
F
15
E
15
D