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WorksheetsFinal Exam Review (PSGA Sem1)
Total questions: 55
Worksheet time: 3hrs 43mins
ML ⊥ LN, LP ⊥ MN, m∠N = 32. Find m∠MLP.
32
58
48
22
Which conjecture is always true based on the following information? ∠S is complementary to ∠T, ∠S is complementary to ∠R.
∠T is complementary to ∠R
∠T is adjacent to ∠R
∠T ≅ ∠R
None of these
Given: QR ≅ ST, QS = 5x + 17, RT = 10 – 2x, and RS = 3, then Find QS.
25
22
19
12
Which of the following cannot be reached as a conclusion? Given: ∠AEN ≅ ∠NEG ≅ ∠GEL
EN bisects ∠AEG
EN and EG trisect ∠AEL
∠AEG is a right angle
∠AEG≅ ∠NEL
AB ⊥ BC. Angle B is divided into three angles in the ratio of 1:2:3 respectively. Find the measure of the largest angle B.
30
10
15
45
If one of the two complementary angles is 40° larger than the other, then the measure of the larger is:
A. 40°
B. 50°
C. 65°
D. 75°
E. None of these
The property which supports the fact that if AB≅CD and CD≅EF , then AB≅EF is ...
Reflexive
Symmetric
None of these
∠4 = 64° and ∠1 = 90°. Find the m∠3.
116
26
64
24
Which transformation rule below translates points 5 units to the left and 2 units up?
(x, y) → (x + 5, y + 2)
(x, y) → (x - 5, y - 2)
(x, y) → (x + 5, y - 2)
(x, y) → (x - 5, y + 2)
The ratio of the angles of a triangle is 2:3:7. Find the measure of the supplement of the largest angle.
75
30
105
45
15
If the angles of a triangle are x°, y°, and (x + y)°, the triangle must be:
isosceles
equilateral
obtuse
right
acute
If the vertex angle of an isosceles triangle is 40°, then each base angle is:
70°
140°
40°
20°
50°
A triangle with no congruent segments is called (a) .
Scalene
Isosceles
Obtuse
Acute
Find the circumcenter of a triangle with coordinates K (2, 1), E (7, 1), and W (2, -5)
(2, 1)
(4.5, 3)
(2, 3)
(4.5, -2)
(11/3, 7/3)
The incenter of a triangle is the point of concurrency of all the….?
angle bisectors
perpendicular bisector
medians
altitudes
none of the above
Find the centroid of a triangle with coordinates K (2, 1), M (7, 1), and F (2, -5).
(2, 1)
(4.5, 3)
(2, 3)
(4.5, -2)
(11/3, -1)
Use ΔQRS, where A, B, and C are the midpoints of the sides. CA = 3x – 1 and SR = 5x + 4, what is CA?
6
8.5
12
17
34
Determine which set of numbers can be the measure of the sides of a triangle.
A. 13, 10, 16
B. 1, 2, 3
C. 5.2, 11, 4.9
D. 208, 9, 219
Which of the following is a criterion for triangle congruence?
SSS
SAS
ASA
All of the above.
For a triangle, which two points of concurrence could be located outside the triangle?
incenter and centroid
centroid and orthocenter
incenter and circumcenter
circumcenter and orthocenter
If the rays of one angle are opposite the rays of another angle, then the angles are:
adjacent angles
corresponding angles
vertical angles
alternate interior angles
consecutive angles
The difference between the supplement and complement of any acute angle is:
45 degrees
90 degrees
135 degrees
180 degrees
It depends on the size of the angle
Which of the following is not a method for proving triangles congruent?
ASA
AAS
SAS
SSA
SSS
Two lines will be perpendicular if they intersect to form:
congruent adjacent angles
complementary angles
vertical angles
supplementary angles
congruent corresponding angles
What theorem justifies the statement WX > ST?
Hinge Theorem
Converse of the Hinge Theorem
Triangle Longer Side Theorem
Triangle Inequality Theorem
List the sides of ΔDEF in order from shortest to longest.
a) FD, EF, DE
b) DE, EF, FD
c) FD, DE, EF
d) EF, FD, DE
Given ΔABC, BC is the perpendicular bisector of AD. Which statement cannot always be proven?
AC ≅ DC
BC ≅ CD
∠ACB ≅ ∠DCB
ΔABC ≅ ΔDBC
Match the following triangle properties with their descriptions:
Circumcenter
Intersection of perpendicular bisectors
Incenter
Intersection of angle bisectors
Centroid
Intersection of medians
Orthocenter
Intersection of altitudes
List the angles of △ABC in order from smallest to largest.
∠B, ∠A, ∠C
∠B, ∠C, ∠A
∠C, ∠A, ∠B
∠C, ∠B, ∠A
What is the measure of ∠TWX?
22°
44°
42°
84°
Find x on the diagram at the right.
100
120
80
60
20
Which graph represents a reflection in the x-axis? A, B, C, or D?
A
B
C
D
Which mapping represents a rotation of 90° counterclockwise about the origin of the point (x, y)?
(x,y)→(-x,y)
(x,y)→(x,-y)
(x,y)→(-y,x)
(x,y)→(y,-x)
In a given triangle, the point of intersection of the three medians is the same as the point of intersection of the three altitudes. Which classification of the triangle is correct?
scalene
isosceles
equilateral
right isosceles
Match the following transformations with their effects:
Rotation
Turns around a point
Reflection
Flips over a line
Translation
Moves without rotating
Dilation
Changes size
The lengths of the sides of a triangle are in the ratio 3:4:5. If the perimeter is 132, find the shortest side.
3
11
12
33
none of these
Match the following transformations with their descriptions:
Reflection
Flipping a figure over a line
Translation
Moving a figure without rotating or flipping it
Dilation
Enlarging or reducing a figure
Rotation
Turning a figure around a point
If RL is parallel to MN, the angle 2 is _ (a) .
180 + a + b
b - a
Match the following:
Two points on a circle are equidistant from the center.
True
The supplement of an angle can be obtuse.
True
An altitude of a triangle bisects an angle of the triangle.
False
If 2 triangles have their corresponding sides congruent, then their corresponding angles are congruent.
True
The base angles of an isosceles triangle are obtuse.
False
What is the measure of ∠VRW if QR⊥ST ?
90 - x
90 + x
x - 90
180 - x
135
Write the converse of: "If an angle is 45°, then it is an acute angle."
If an angle is not 45°, then it is not acute.
If an angle is not acute, then it is not 45°.
If an angle is acute, then its measure is 45°.
What is the slope of a line parallel to a line with a slope of ¾?
4/3
-4/3
-3/4
-1
None of these
Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. A(2,1), B(4,1), C(4,-3) after dilation D: (x,y) → (4x,4y).
A'(0.5, 0.25), B'(1, 0.25), C'(1, -0.75)
A'(8, 4), B'(16, 4), C'(16, -12)
If the perimeter of ΔEFG is 32, is ΔEFG scalene, isosceles, or equilateral?
scalene
isosceles
equilateral
If 2 parallel lines are cut by a transversal, then corresponding angles are:
supplementary
congruent
vertical
If 2 parallel lines are cut by a transversal, then the alternate exterior angles are:
congruent
supplementary
complementary
vertical
none of the above
A base angle of an isosceles triangle is 4 times the vertex angle. Find the measure of an exterior angle at the base.
70°
100°
140°
30°
Find x in the diagram where two parallel lines are intersected by a transversal, creating angles of 110° and 30°.
40°
150°
100°
70°
Three sides lengths of a triangle are in the ratio of 2:5:7. If the perimeter is 112, find the longest side length.
A) 28
B) 56
C) 42
D) 49
No such triangle exists.
In rectangle RECT, m∠R = 4x + 2. Find 2x.
44
46
48
50
The measure of the supplement of an angle is 3 times the measure of the complement of the angle. Find the measure of the supplement.
90 degrees
45 degrees
135 degrees
180 degrees
What is the transformation described by the function M: (x, y) → (x + 4, y - 6)?
Translation
Reflection
Rotation
Dilation
The image of point J under a 180° rotation about the origin is (7, -3). The coordinates of point J are (a) .
(-7, 3)
(7, 3)
(-7, -3)
(3, -7)
Fill in the blank: The possible lengths of the third side of a triangle, given the lengths of the other two sides are 8 cm and 10 cm, are between (a) .
3 cm and 17 cm
4 cm and 16 cm
Fill in the blank: In triangle PQR, QM is both an altitude and a median. Therefore, triangle PQR must be (a) .
Equilateral
Isosceles
Scalene
Right-angled
