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Leandra Morgan
EDU 250/ 10:50am
Grade 8
Geometry
Content Standard 3.0 The student will develop an understanding of geometric concepts and
relationships as the basis for geometric modeling and reasoning to solve problems involving one, two-, and three-dimensional figures.
Accomplishments
8.3.1 Analyze characteristics and properties of two- and three-dimensional geometric figures.
a. understand relationships among the angles (e.g., complementary, supplementary,
interior, exterior, vertical, corresponding);
8.3.3 Apply transformations and use symmetry to analyze mathematical situations.
a. describe sizes, positions, and orientations of shapes under transformations (e.g.,
rotations, translations, reflections, dilations);
b. relate symmetry and congruence to reflections about a line.
Facts:
1. Architects must use very precise angle measurements when constructing building plans
and engineering intersections. Buildings are generally constructed using right angles.
2. At 9 o’clock, the hands of the clock form a right angle because the angle measures 90
degrees.
3. At 6:22, morning or evening, the hands of the clock form an acute angle because it
measures less than 90 degrees.
4. An obtuse angle is one that measures between 90 and 180 degrees.
5. Supplementary angles are angles whose sum equals 180 degrees; when placed adjacent to
one another, they form a straight line.
6. The angle made by the ray pointing upward (upper part of the second hand) and the
minute hand and the angle made by the ray pointing downward (lower part of the second
hand) and the hour hand are vertical angles because they have equal degree
measurements and are opposite one another.
7. At this moment in time, the second hand is an angle bisector because it splits the larger
angle formed by the minute and hour hands into two equal angles.
8. The frame of this hourglass possesses both a vertical and horizontal line of symmetry.
9. Thinking of the first knob as the original position, the third knob has been rotated
approximately 270 degrees (-90 degrees).
10. The orange watch has undergone the transformation of dilation.
11. An original shape and its dilation are said to be “similar” because they possess the same
angle measurements (not changing form), but are different sizes.
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Leandra Morgan
EDU 250/ 10:50am
Vocabulary Words:
1. angle: two rays that intersect at an endpoint called the vertex form an angle
2. right angle: an angle that measures 90 degrees
3. acute angle: an angle that measures between 0 and 90 degrees.
4. obtuse angle: an angle that measures between 90 and 180 degrees
5. complementary angles: angles whose sum equals 90 degrees
6. supplementary angles: angles whose sum equals 180 degrees
7. vertical angles: a pair angles whose degree measurements are equal that are formed on
opposite sides of the point at which two lines intersect
8. angle bisector: a ray that divides an angle in half, creating two angles of equal degree
measurements
9. symmetry: a correspondence in the position of pairs of points of a geometric object that are
equally positioned about a point, line, or plane that bisects the object
10. transformation: (in this mathematics course) the alteration of a geometric shape by a rotation,
reflection, translation, or dilation
11. rotation: a transformation in which a point, line, or geometric shape is rotated by a specific
angle measurement about a fixed point.
12. dilation: transformation in which a geometric object is enlarged or contracted
Questions:
1. What is an angle? Geometric figure formed by the intersection of two rays
2. What is an angle bisector? a ray that divides an angle in half, creating two angles of equal
degree measurements
3. On an angle, what is the point called where the rays intersect? vertex
4. Contrast complementary and supplementary angles. The sum of complementary angles forms
90 while the sum of supplementary angles forms 180. OR Complementary angles form a right
angle and supplementary angles for a straight line.
5. Give an example of an obtuse angle. Explain why the angle you chose is classified as obtuse.
An angle that measures 135 degrees is obtuse because 90< 135< 180
6. What is a right angle? an angle that measures 90 degrees
7. At 6:00, the angle created by the minute and second hand “rays” and the angle created by the
hour and second hand “rays” are called what? Supplementary angles
8. What are vertical angles? a pair angles whose degree measurements are equal that are
formed on opposite sides of the point at which two lines intersect
9. Define symmetry. a correspondence in the position of pairs of points of a geometric object
that are equally positioned about a point, line, or plane that bisects the object
10. On a clock, if the second hand points to “11” and the hour hand points to “1”, toward what
number would the minute hand need to point in order to be called an “angle bisector? The 12 or
the 6.
11. Why may it be said that “The orange watch has undergone the transformation of dilation”?
The magnifying glass ENLARGED the object.
12. Give three examples of a transformation. Rotation, reflection, rotation, or dilation
13. Besides the hourglass, name three other objects that generally possess vertical AND
horizontal lines of symmetry. A five-point star, a window, the back of a playing card. (Answers
will vary)
14. What is a transformation in which a geometric object is enlarged or contracted? Dilation
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Leandra Morgan
EDU 250/ 10:50am
15. An angle is formed by the intersection of what? Rays
16. What is the term for an angle that measures between 0 and 90 degrees? Acute
17. How many pairs of vertical angles are formed by intersecting lines? Two
18. It will appear that no transformation has occurred if an object is rotated ____degrees. 360
19. At 6:22, the hands of the clock form a(n) _____angle. Acute
20. Most structures in our society like buildings are created using primarily what kind of angles?
right
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