Download A Geometric Look at the World KEY

Geometry
HS Mathematics
Unit: 01 Lesson: 01
A Geometric Look at the World KEY
1. A sheet of card stock is folded and creased so that two flat surfaces form an angle.
Describe this situation geometrically.
The intersection of two planes is a line. The crease represents the line and the two
surfaces on either side of the crease are the planes.
2. A flagpole is positioned in the center of a flat courtyard of brick pavers. Describe this
situation geometrically.
The intersection of a line and a plane is a single point. The flagpole is the line and the
courtyard is the plane.
3. Using the definitions for parallel and skew lines, explain how critical attributes play a role
in distinguishing the two.
Without the critical attribute of coplanar in the definition for parallel, the definitions would
be the same.
4. Consider the town of Junction along Interstate 10 at mile marker 456. Describe the
position(s) of any such places 120 miles from Junction in terms of the Interstate mile
marker system by using W for the location to the west of Junction and E for the location
east of Junction. Use J to indicate Junction. Sketch a diagram depicting the situation.
Two locations will be 120 miles away from Junction.
J
Junction
456
576
336
120 miles
120 miles
W
E
5. Write the Segment Addition Postulate for the above situation using the points W, J, and E
to name segments.
WJ + JE = WE
6. What length does the segment WE represent?
240 miles
7. What lengths do the segments WJ and JE represent? How do they relate to the length
represented by WE? What can you conclude about the length represented by segment
WJ and the length represented by segment JE?
Both are 120 miles. They are both ½ of WE. The segments are equal.
8. What do the previous answers lead you to believe about point J?
Point J is the midpoint of segment WE.
©2012, TESCCC
05/15/12
page 1 of 3
Geometry
HS Mathematics
Unit: 01 Lesson: 01
9. Since WJ = JE, what two ways could the Segment Addition in #5 be rewritten using
substitution?
WJ + WJ = WE or JE + JE = WE
A Geometric Look at the World KEY
Use the scenario below to answer the following questions.
The drawbridge that spans Descartes’ Bay (named after a Frenchman named Rene Descartes)
is raised by two sets of hydraulic cylinders. The hydraulics raise the bridge to two different
positions. The first set raises each side of the bridge from level up to an incline of (5x – 8)
degrees above horizontal. The second set then raises the bridge the rest of the way or (4x + 8)
degrees more to a position perpendicular to the level position.
10. Sketch a diagram of angles depicting one side of the bridge at each of the three positions,
level, after the first set of cylinders has raised it, and in the fully raised position. Label the
angles in your diagram and include the dimensions given in the above scenario.
(5x – 8)o
(4x + 8)o
11. What angle does each side of the bridge make when fully raised from the level position?
90 degrees or a right angle
12. What is the relationship between the two angles through which the hydraulic cylinders
raise the bridge?
They are complementary.
13. Write the Angle Addition Postulate for the scenario. Solve for x and find the value for each
angle.
(5x – 8) + (4x + 8) = 90
x=10
(5x – 8) = (5*10 – 8) = 42º
(4x + 8) = (4*10 + 8) = 48º
©2012, TESCCC
05/15/12
page 2 of 3
Geometry
HS Mathematics
Unit: 01 Lesson: 01
©2012, TESCCC
05/15/12
page 3 of 3