Download HG Midterm Review

Honors Geometry Midterm Review
Part 1 - Always (A), Sometimes (S), Never (N)
1) The supplement of an acute angle is an obtuse angle.
2) If AB is the perpendicular bisector of CD , then CD is the perpendicular bisector of AB .
3) Two lines perpendicular to the same line are perpendicular to each other.
4) The bisector of an angle of a triangle bisects the side opposite the angle.
5) If two triangles have all their corresponding angles congruent, then their corresponding
sides are congruent.
6) If the m∠X < m∠Y, then the supplement of ∠X is greater than the supplement of ∠Y.
Part 2 – Multiple Choice
W
1) Which of the following may be assumed from the diagram?
a. ∠WXY is a right angle
b. Z is the midpoint of WY
Z
c. ∠WZX is a right angle
d. ∠Y is acute
e. None of these
Y
2) Which of the following is false?
a. AB  AB
b. AB  BA
c. AB  BA
d. AB = BA
e. All of these
3) If ∠1 is supplementary to ∠2, ∠3 is supplementary to ∠4, and ∠2 = ∠4, then:
a. ∠1  ∠3
b. ∠1  ∠2
c. ∠1  ∠4
d. ∠1 is supplementary to ∠3
e. ∠2 is supplementary to ∠4
X
4) In the diagram, AB  DE and ∠A  ∠D. In order to conclude that ABC  DEF
by ASA, it is necessary to know that:
A
D
a. ∠B  ∠E
b. ∠ACB  ∠DEF
c. ∠ABC  ∠DFE
d. ∠ABC  ∠DFB
e. ∠DFB  ∠ACE
B
F
C
E
5) If the measure of an angle exceeds its supplement by 20o, then the measure of the angle
is:
a. 100o
b. 80o
c. 55o
d. 35o
e. 125o
6) In order to prove that a point lies on the perpendicular bisector of a segment, it is
necessary to show:
a. The point is on the segment
b. The distance from the point to the endpoints of a segment is equal
c. The point is the midpoint of the segment
d. The point is the perpendicular bisector of the segment
e. All of the above
7) If two angles are congruent and supplementary then the angles must be:
a. Adjacent angles
b. Acute angles
c. Obtuse angles
d. Straight angles
e. Right angles
8) If the vertex angle of an isosceles triangle is 40o, then each of the base angles is:
a. 70o
b. 140o
c. 40o
d. 20o
e. 50o
E
9)
Given the diagram as marked with AB || CD , then ∠AFE equals:
a. 162o
b. 164o
c. 18o
d. 16o
e. 57 1/7o
A
C
F
1/2x + 10
G
H
3x - 30
B
D
10) If the angles of a triangle are xo, yo, and (xo + yo), the triangle must be a(n):
a. Isosceles triangle
b. Equilateral triangle
c. Obtuse Triangle
d. Right triangle
e. Acute triangle
A
11) Given the diagram as marked, find m∠ACB.
a. 23o
b. 102o
c. 42o
d. 78o
e. none of these
D
2x+10
6x-18
3x - 2
C
B
12) Which of the following is not a correct method of proving congruent triangles:
a. SAS
b. ASA
c. SSA
d. SSS
e. HL
13) In the diagram below, which of the following is not always true:
a. b + c + d = 180o
b. c = d
b
c. a = b + c
d. a + d = 180o
e. all are always true
a
d
c
Part 3 – Matching
Left
<, >, =, OR impossible
Right
Sum of the measures of the interior angles of a
triangle
180o
m 1
30o
1
128o
Slope of BA
A (0, 8)
2
C (6, 0)
(-8, -6) B
a+b+c
x+c
a
b
c x
A
Part 5 - Proofs
Given: AE  BD
C is the midpoint of BD
D
B
C
DE  AB
Prove: C is the midpoint of AE
E
B
Given: AB  BC  CD  DA
Prove: AC is  bisector to BD
and
BD is  bisector to AC
C
E
A
D
A
Given: ∠ABE≅ ∠AEB
BC  ED
Prove: BD  EC
B
C
Given:  ABC is isosceles with base BC
D and E trisect BC
∠1≅ ∠2
E
D
B
D 1
3
M
A
Prove: ∠3≅ ∠4
E 2
C
4
N
DA≅CB
Part 4 – Algebra Practice
In Exercises 1, point M is between L and N on LN. Use the given information to write
an equation in terms of x. Solve the equation (disregard any answers that do not make
sense in the context of the problem). Then find LM and MN.
1.
LM = x2
MN = x
LN = 56
Find the values of x-and y.
2.
4.
3.
5.
3
Tell whether the lines through the given points are parallel, perpendicular, or neither.
6. Line 1: (–5, 6), (–2, 2)
Line 2: (4, 2), (7, 6)
7. Line 1: (–4, 8), (6, 2)
Line 2: (–4, 1), (–1, 6)
8.
Line 1: (–7, –4), (5, 7)
Line 2: (2, 3), (14, 14)
9.
Line 1: (–5, –3), (6, 3)
Line 2: (1, 9), (7, –2)
Find the coordinates of the midpoint of the segment with the given endpoints.
10.
S (4, –1) and T (6, 0)
11.
L (4,2) and P (0, 2)
The endpoints of two segments are given. Find each segment length.
Tell whether the segments are congruent.
12. AB : A (2, 6), B (0, 3)
CD: C (–1, 0), D (1, 3)
Find the values of x and y.
13.
14.
Find the values of x and y.
15.
16.
x
3y
50ׂ
y
2x
17. Find the values of x, y, and z
18.
Find the perimeter of the triangle.
Find the values of x and y, if possible. If not possible, explain your reasoning.
19.
20.
21.An image and its translation are given.
Sketch the original figure:
22. Solve for x:
23.
a.
b.
24. Point L is the centroid of NOM. Use the given information to find the value of x.
a. OL = 8x and OQ = 9x + 6
b. NL = x + 4 and NP = 3x + 3
c. ML = l0x – 4 and MR = 12x + 18
24. A logo to be placed on the cabin is being designed using the triangles to the right. Are the triangles
congruent? Construct a mathematical argument to justify your answer.
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b. Mrs. Dias decided to connect points A and D to create a different design. What is the best
classification for the new triangle created - ΔABD? How do you know?
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