Download Angle A - White Plains Public Schools

Name: ___________________________ Per: _______ Date: ______________
State Test Review Day 1: Parallel Lines and Angles and Transformations
WHAT DO YOU NEED TO KNOW?
Notes to read very carefully before starting!!!!! Complete the examples problems as well.
1) When two parallel lines are cut by a transversal, 8 angles are formed.
1
3
2
5
IF YOU PICK ANY TWO, THERE ARE ONLY 2
OPTIONS… THEY ARE EITHER GOING TO BE
CONGRUENT (EQUAL) OR SUPPLEMENTARY!
4
7
6
8
If they are equal, there are 4 different kinds of
Equal angles.
Vertical Angles – Angles that are across from each other in an
. 6 and 7 or 1 and 4.
Corresponding Angles – Angles that would match up if we slid the top group of angles down
onto the bottom group of angles.
2 and 6 or 3 and 7.
Alternate Interior Angles – Angles that are inside the parallel lines but are on opposite sides
of the transversal. 3 and 6 or 4 and 5. (Diagonal Jump)
Alternate Exterior Angles – Angles that are outside the parallel lines but are on opposite
sides of the transversal. 1 and 8 or 2 and 7. (Diagonal Jump)
2) Complimentary angles add up to 90 degrees; supplementary angles add up to 180 degrees.
A way to remember the difference is, C comes before S, and 90 comes before 180.
3) DON’T FORGET – If you are given angles in the form of equations, once you solve the
equation for x, you might not be done. The question may be asking for the angle
measurement, which means you still have to plug your answer in.
Example 2x
4x
2x + 4x = 90
6x = 90
x = 15
x is 15, but in order to find the angles,
you need to plug back in. So the angles
are 2(15) = 30° and 4(15) = 60°
Multiple Choice Questions – NO CALCULATOR!!!!!!!!!!!!!
1) Angles 1 and 2 are adjacent on a straight line. What is the sum of the measures of the
angles?
A. 30°
C. 90°
B. 60°
D. 180°
2) When two lines intersect, 4 angles are formed. If one of the angles is 68°, what are the
other three angles?
A. 68°, 68°, 68°
C. 68°, 112°¸112°
B. 68°, 22°, 22°
D. 68°, 68°¸112°
3) In the picture to the right, if the measure of angle x = (2y + 30) °, what is y ?
A. 21.5
C. 68
B. 25
D. 80
80°
x
4) Based on the drawing below, which of the following statements is true?
y
x
A. x and 123°are supplementary
C. x and y are congruent
123°
57°
B. y and 123° are supplementary
D. x and 57° are congruent.
5) Suppose mr = (4x + 20) ° and ms = (x + 60) °. If r and s are supplementary angles,
find the measure of the smaller angle.
A. 20°
C. 80°
B. 60°
D. 100°
6) Angles x and y are alternate interior angles formed by two parallel lines and a transversal.
If mx = 167°, what is the my?
A. 13°
C. 180°
B. 77°
D. 167°
7) Which of the following statements is true?
A. All interior angles are congruent
C. Same side exterior angles are congruent
B. All exterior angles are congruent
D. Alternate exterior angles are congruent.
8) Angle T measures 149°. What is the measure of corresponding angle S formed by parallel
lines and a transversal?
A. 31°
C. 149°
B. 59°
D. 180°
Use the following diagram to answer the next two questions.
9) Which equation best describes the relationship between angles
1 and 8
A.
B.
C.
D.
1 +
1 +
1 +
1 +
8 = 180
8 = 90
8 = 4 + 5
8 = 3 + 6
1 2
3 4
10) Which statement is true about
A.
B.
C.
D.
7
56
8
1 and 2 are congruent
4 and 6 are complimentary
1 and 5 are supplementary
4 and 5 are congruent
Open-Ended Questions – Use a CALCULATOR!!!!!!!!!!!!!
1) D and E are supplementary angles. The mD = (5x + 8) and the mE = (2x – 3).
Write and solve an equation to find the value of x and the measure of each angle.
x = _______
mD = ______
mE = ______
2) Given mDBC = (3x + 5) and mABD = 5(x + 1)
Find the value of x = ________ and the m ABD = ________
A
D
5(x + 1)
B
3x + 5
C
3) Angle A and angle B are supplementary. In addition, angle A is complementary to angle C.
What are the measures of angle A and angle C if the angle B measures 137?
Angle A = ________________ degrees
Angle C = ________________ degrees
4) Line z and line w are parallel lines cut by the transversals, line x and line y,
which are parallel. The m4 = (8x – 20) and m13 = (6x + 8).
Part A: Write and Solve an Equation to find the value of x = _________
Part B: Find the m4= _____ and m13= ______.
Part C: What is the m2= _____ and m7= ______.
Transformational Geometry
WHAT DO YOU NEED TO KNOW?
Notes to read very carefully before starting!!!!! Complete the examples problems as well.
1) A transformation is when you change an objects orientation, location, or size. There are 4
kinds of transformations.
2) A Translation is when you move an object up, down, left or right. Size and orientation do not
change.
B
A
Example – Figure A has been translated to the right and up.
3) A Rotation is when you rotate a figure around a point (usually the origin). The orientation
changes but not the size.
A
B
Example – Figure A has been rotated 90 degrees clockwise.
DON’T FORGET – Turn the page the given number of degrees to reveal the ANSWER!!!
4) A reflection is when a figure is reflected “over” or “in” a line of symmetry (usually the x or
y-axis).
A
B
Example – Figure A has been reflected in the y - axis.
5) A dilation is when the figures points are multiplied by a scale factor to make the figure
bigger or smaller. This is the only transformation that changes the figures size.
Example – If triangle ABC has coordinates A(3, 4), B(1, 0) and C(-2, 3), what will the
coordinates of the new figure be after a dilation of scale factor of 3?
A’ __________________ B’ __________________ C’ __________________
Multiple Choice Questions – NO CALCULATOR!!!!!!!!!!!!!
1) What would the point (6, -3) be after it
has been rotated 90 degrees?
2) What would the point (2, -5) be after it
has been reflected in the y-axis?
a) (-6, -3)
c) (-3, 6)
a) (2, -5)
c) (-2, 5)
b) (6, 3)
d) (3, 6)
3) What would the point (6, -3) be after it
has been rotated 180o?
a) (-6, -3)
c) (-3, 6)
b) (-6, 3)
d) (3, 6)
5) If a figure is dilated by a scale factor of
½…
a)
b)
c)
d)
The side lengths will be 5 units longer
The side lengths will be half the size
The side lengths will be 5 times longer
The side lengths will be 0.5 units longer
7) Triangle ABC has coordinates A(-5, -3),
B(-5, -5) and C(-1, -5). What will be the
coordinates of point C, after a dilation of
scale factor of 3?
a)
b)
c)
d)
C’ (-15, -3)
C’ (-3, -15)
C’ (15, -3)
C’ (3, 15)
b) (-5, 2)
d) (-2, -5)
4) Which best describes the translation for:
(x,y)
(x + 3, y - 1)
a)
b)
c)
d)
3 units left and 1 down
3 units right and 1 down
3 units right and 1 up
1 unit right and 3 up
6) Which of the following transformations
does not result in a congruent figure?
a) reflection
c) rotation
b) dilation
d) translation
8) The point N(-6, 4) is translated to
N’(-2, -2). Which rule would describe this
translation?
a)
b)
c)
d)
(x, y)
(x, y)
(x, y)
(x, y)
(x + 4, y + 6)
(x - 4, y + 6)
(x + 4, y - 6)
(x - 4, y - 6)
9) Name the coordinates of the image of
point Y(-2, 5) after it has been reflected in
the x-axis.
10) The point Q(3, 4) has been translated
right 3 units and down 2 units. What are the
coordinates of the image point?
a)
b)
c)
d)
a)
b)
c)
d)
(-2, -5)
(2, -5)
(0, 5)
(-2, 0)
Q’ (0, 2)
Q’ (6, 6)
Q’ (0, 6)
Q’ (6, 2)
Open-Ended Questions
1) Part A: On the grid, graph and label ∆ABC
with vertices A(-3, 1), B(-3, 4), and C(-1, 1).
Part B: Reflect this triangle in the x-axis.
Record the new points.
A’(
,
)
B’ (
,
)
C’ (
,
)
Part C: Perform a dilation on ∆ABC using a scale
factor of 2. Label the coordinates on the new
figure.
Part A: On the grid below, graph and label
∆ABC with vertices A(4, 0), B(9, 0) and C(6, 4).
Part B: Translate this triangle up 5 units and
to the left 2 units. Record the new points.
A’(
,
)
B’ (
,
)
C’ (
,
)
Part C: Rotate ∆A’B’C’ 90 degrees clockwise.
Label the coordinates on the new figure.