Download Interior Angles

Name:_________________________________________________________ Period:___________ Date:___________________________
Marking Period I Exam Study Guide 2014-2015
Part 1:
8.G.1: Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same
length. Angles are taken to angles of the same measure. Parallel lines are taken to parallel lines.
8.G.2: Understand that a two-dimensional figure is congruent to another if the second be obtained from the first by a sequence of rotations, reflections, and
translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.3: Describe the effect of dilations, translations, rotations, and reflections, on two-dimensional figures using coordinates
8.G.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections,
translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Transformations
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Translations:
1.) Translate the figure 8 units to the right and 10 units up on the graph and label appropriately.
a.
What happened to the size? ________________________
b.
What happened to the shape? ________________________
c.
What happened to the orientation? ______________________
d.
What happened to the x-coordinate? ______________________
e.
What happened to the y-coordinate? ______________________
f.
Is the pre-image and image similar or congruent?
___________________________
2.) a. Explain in words how the pre image can be transformed into the image.
(Use mathematical terms to describe the transformation.)
b. Are these figures similar or congruent?
3.) If this shape was translated 5 units right and 9 units up, draw what its orientation would look like.
4.) Describe how many units a figure will move horizontally and vertically when translated according to
the rule (x,y)  ( x + 5 , y – 8 )
5.) Pre-image vertices: A ( -1, 2) B (-5, 6) C (-2, 7)
Image vertices: A’ ( 5, 0) B’ (1, 4) C’(4, 5)
a. Identify how the pre-image was transformed to the image
b. Are these two figures are similar or congruent?
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Reflections:
6.) Reflect the figure over the y-axis on the graph and label appropriately.
a.
What happened to the size? ________________________
b.
What happened to the shape? ________________________
c.
What happened to the orientation? ______________________
d.
What happened to the x-coordinate? ______________________
e.
What happened to the y-coordinate? ______________________
f.
Is the pre-image and image similar or congruent?
___________________________
7.) Reflect the figure over the x-axis on the graph and label appropriately.
a.
What happened to the size? ________________________
b.
What happened to the shape? ________________________
c.
What happened to the orientation? ______________________
d.
What happened to the x-coordinate? ______________________
e.
What happened to the y-coordinate? ______________________
f.
Is the pre-image and image similar or congruent?
___________________________
8.) a. Explain in words how the pre image can be transformed into the image.
(Use mathematical terms to describe the transformation.)
b. Are these figures similar or congruent?
9.) If this shape was reflected over the x-axis, draw what its orientation would look like.
10.) If this shape was reflected over the y-axis, draw what its orientation would look like.
11.) Describe how the figure will move when reflected with the rule (x,y)  ( -x, y)
12.) Pre-image vertices: A ( -1, 3) B (2, 2) C (4 , 5)
Image vertices: A’ ( -1, -3) B’ (2, -2) C’(4, -5)
a. Identify how the pre-image was transformed to the image
b. Are these two figures are similar or congruent?
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Rotations:
13.) Rotate the figure 90 degrees clockwise on the graph and label appropriately
a.
What happened to the size? ________________________
b.
What happened to the shape? ________________________
c.
What happened to the orientation? ______________________
d.
What happened to the x-coordinate? ______________________
e.
What happened to the y-coordinate? ______________________
f.
Is the pre-image and image similar or congruent?
___________________________
14.) a. Explain in words how the pre image can be transformed into the image.
(Use mathematical terms to describe the transformation.)
b.) Are these figures similar or congruent?
15.) If this shape was rotated 180 degrees clockwise, draw what its orientation would look like.
16.) Describe how the figure will move when reflected with the rule (x,y)  ( y, -x)
17.) Pre-image vertices: A ( -2, 3) B (3, 3) C (6 , 8)
Image vertices: A’ ( -2, -3) B’ (-3, -3) C’(-6, -8)
a. Identify how the pre-image was transformed to the image
b. Are these two figures are similar or congruent?
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Dilations:
Scale Factor:
In order to calculate scale factor, create a ratio of corresponding sides of the image to the pre-image.
Ratio to calculate scale factor: IMAGE__
PRE-IMAGE
3
18.) Dilate the figure with a scale factor of 4 on the graph and label. Write the new coordinates.
g.
What happened to the size? ________________________
h.
What happened to the shape? ________________________
i.
What happened to the orientation? ______________________
j.
What happened to the x-coordinate? ______________________
k.
What happened to the y-coordinate? ______________________
l.
Is the pre-image and image similar or congruent?
___________________________
19.) Dilate the figure by a scale factor of 2.5 with the origin as the center of dilation.
Write the new vertices of the image.
20.) a. Explain in words how the pre image can be transformed into the image.
(Use mathematical terms to describe the transformation.)
b. Are these figures similar or congruent?
21.) Describe how a figure will transform with the rule (x,y)  ( 4x, 4y)
22.) Pre-image vertices: A ( -2, 3) B (3, 3) C (6 , 8)  Image vertices: A’ ( -1, 1.5) B’ (1.5, 1.5) C’(3, 4)
a. Identify how the pre-image was transformed to the image
b. Are these two figures are similar or congruent?
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Combining Transformations:
23.) Specifically, how can rectangle A be transformed to become triangle B? (Include rules as proof)
Transformation Sequence Steps:
1. Apply the given transformation on the pre-image to create an image (label prime’)
2. Apply the next given transformation on the IMAGE (label double prime”)
3. Continue to apply given transformations on the newest images
24.) a. Label the pre-image “Figure 1”
b. -Translate Figure 1 four units right and five units up
- reflect over y-axis and label Figure 2
c. Reflect Figure 2 over the x-axis and label Figure 3
d. Dilate Figure 3 by a scale factor of two and label Figure 4
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Part 2:
8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles
Interior/Exterior Angles of Triangles:
Interior Angles:
25.) Solve for the missing angle:
26.) If y = 28°, what is the value of x?
27.) Solve for the exterior angle
28.) Solve for the missing remote interior angle
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Angle-Angle Similarity Postulate of Triangles:
#29-32 explain why or why not the following pairs of triangles are similar or not similar.
29.)
30.)
31.)
32.)
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Angle Relationships
Vertical Angles
A pair of angles opposite angles formed by
intersecting lines. These angles share a vertex,
but DO NOT share a side;
CONGRUENT
Ex: b & d; and a and c
Alternate Interior Angles
A pair of angles formed by a transversal and
parallel lines. These are nonadjacent angles
located in between the parallel lines on opposite
sides of the transversal;
CONGRUENT
Ex: r & v; and s and t
Corresponding Angles
A pair of angles formed by a transversal and
parallel lines. These angles are in the same
position in a different location (match up);
CONGRUENT
Ex: m & q;
n and r;
o & s; p and
Alternate Exterior Angles
A pair of angles formed by a transversal and
parallel lines. These are nonadjacent angles
located outside parallel lines on opposite sides of
the transversal;
CONGRUENT
Ex: a & d; and b and c
t
Same Side Interior Angles
A pair of angles formed by a transversal and
parallel lines. These angles are in between the
parallel lines and on the SAME side of the
transversal;
SUPPLEMENTARY (add up to 180)
Ex: x & y
33.) a. Determine the angle measures for angles 1-8 and justify your reasoning.
b. Name all angles supplementary to angle 1
c. Name all angles congruent to angle 1
34.) In the figure line m is parallel to line q. Measure of angle 7 is = 80 and the measure
of angle 4 is = 3x + 40. Find the measure of angle 4 and explain your reasoning.
35.) If the figure if line l is parallel to line m, what is the value of x + y in degrees?