Unit 2 Stations - Unit 1 Review

Which of the following best explains the difference between a conjecture and a theorem?

• A conjecture is a claim justified by logic and mathematics. A theorem is a claim justified by logic alone.

• A theorem is a claim justified by logic and mathematics. A conjecture is a claim justified by logic alone.

• A conjecture is a claim that is believed to be true but not been proven. A theorem is a claim that has been proven true.

• A theorem is a claim that is believed to be true but has not been proven. A conjecture is a claim that has been proven true.

Andre flipped through an atlas and noticed that each map in the atlas was colored with four colors. Based on what he saw, he thought it was probably true that any map could be colored with four colors. Which of the following best describes Andre's conclusion?

• Conjecture

• Postulate

• Definition

• Theorem

Which of the following is not an undefined term in Euclidean geometry?

• Point

• Polygon

• Plane

• Line

Which of the following best compares parallel lines in Euclidean and spherical geometry?

• In Euclidean geometry, for any line and point not on the line, there exists two parallel lines that pass through the point.

  
  

  In spherical geometry, for any line and point not on the line, no parallel line exists.

• In Euclidean geometry, for any line and point not on the line, there exists one parallel line that passes through the point.

  
  

  In spherical geometry, for any line and point not on the line, there exists two parallel lines that pass through the point.

• In Euclidean geometry, for any line and point not on the line, there exists one parallel line that passes through the point.

  
  

  In spherical geometry, for any line and point not on the line, no parallel line exists.

• In Euclidean geometry, for any line and point not on the line, no parallel line exists.

  
  

  In spherical geometry, for any line and point not on the line, there exists one parallel line that passes through the point.

In Euclidean geometry, some premises, such as "All right angles are congruent," are assumed to be true as a starting point for reasoning. Which of the following best describes such a basic premise?

• Conjecture

• Definition

• Theorem

• Postulate

How do intersecting lines compare in Euclidean and spherical geometries?

• Lines intersect at only one point in both spherical and Euclidean geometries.

• Lines intersect at only one point in Euclidean geometry but do not intersect in spherical geometry.

• Lines intersect at only one point in spherical geometry but at two points in Euclidean geometry.

• Lines intersect at only one point in Euclidean geometry but at two points in spherical geometry.

Sandra uses a compass and straightedge to construct an angle that is congruent to <RST. She performs the steps below:

Mark and label point J. With a straightedge, draw a ray extending from J.

Center compass at vertex S and draw an arc that intersects both rays of <RST.

Using the same compass setting, with center at J, draw an extended arc through the ray and label the point of intersection K.

Which of the following should be the next step of Sandra's construction?

• Use the straightedge to draw a segment extending from J through the arc.

• Set the compass to the distance between the two points of intersection of the arc and rays of <RST.

• Use the straightedge to draw a segment extending from K to the end of the arc.

• Using the same compass setting, with center K, draw an arc that intersects the other arc.

Erika uses a compass and a straightedge to construct a line perpendicular to given line EF. Which of the following shows a construction of a perpendicular line that is one step from being complete?

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Angela uses a compass and straightedge to bisect <PQR shown below. Which of the following shows a construction of the bisector of <PQR that is one step from being complete?

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One ruler is placed on top of another such that the edges of the rulers form a 25 degree angle, as shown. What is the degree measure of the angle labeled x?

• 100

• 115

• 125

• 155