1.
Conjecture: If an obtuse angle is bisected, then the two newly formed congruent angles are______.
Correct Answer
C. Acute angles
Explanation
If an angle more than 90 degrees but less than 180 degrees is created, then each of the two congruent angles must be less than 45, or acute.
2.
If two angles form a linear pair, then ______________________________________
Correct Answer
the sum of their measures is 180 degrees
the sum of their measures is 90 degrees
the size of the angles are congruent
none of the above
Explanation
If two angles form a linear pair, then the sum of their measures is 180 degrees.
3.
If two angles are vertical angles, then their measures are _____________.
Correct Answer
B. Equal
Explanation
Vertical angles are formed when two lines intersect. These angles are opposite each other and have the same measure. Therefore, if two angles are vertical angles, their measures are equal.
4.
What is the definition of a converse?
5.
If two parallel lines are cut by a _________, then corresponding angles are congruent.
Correct Answer
E. None of the above
Explanation
The answer is a transversal.
6.
If a transversal cuts two parallel lines, then alternate interior angles are congruent, and alternate _________ angles are congruent.
Correct Answer
A. Exterior
Explanation
If a transversal cuts two parallel lines, then alternate interior angles are congruent, and alternate exterior angles are congruent. This is a property of parallel lines and transversals. Alternate interior angles are the angles that are on the opposite sides of the transversal and between the two parallel lines. Similarly, alternate exterior angles are the angles that are on the opposite sides of the transversal but outside the two parallel lines.
7.
Is the converse of the Parallel Lines Conjecture (If a transversal cuts two parallel lines, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent) true?
Correct Answer
A. Yes
Explanation
The converse of the Parallel Lines Conjecture states that if a transversal cuts two parallel lines, then the corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent. This statement is true because if two lines are parallel, any transversal that intersects them will create congruent corresponding angles, alternate interior angles, and alternate exterior angles. Therefore, the answer is yes.
8.
When you duplicate an angle, do you ever change the compass setting?
Correct Answer
C. Depends
Explanation
When you measure the distance from one ray to the other, it is usually different from the arc you drew before.
9.
When constructing any parts of geometry, what are the only two tools you can use?
Correct Answer
E. Both a and d
Explanation
The correct answer is "both a and d" because a compass and a straightedge are the only two tools that can be used to construct any parts of geometry. A compass is used to draw circles and arcs, while a straightedge is used to draw straight lines. These two tools are essential in constructing various geometric shapes and figures accurately. A protractor and ruler are not sufficient on their own to construct all parts of geometry.
10.
A median is ___________________________________
Correct Answer
D. The segment connecting the vertex of a triangle to the midpoint of its opposite side
Explanation
A median is the segment connecting the vertex of a triangle to the midpoint of its opposite side.
11.
A midsegment is........
12.
What does equidistant mean?
Correct Answer
same distance
same distance from two points
equal distance
Explanation
Equidistant means that two or more points are the same distance apart. It can refer to the same distance from two points or an equal distance between multiple points. In other words, all the points are equidistant if they are equally spaced from each other or from two specific points.
13.
If a point is on the ________________ bisector of a ____________, then it is equidistant from the endpoints.
Correct Answer
C. Perpendicular, segment
Explanation
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints. This is because the perpendicular bisector is a line that intersects the segment at a 90-degree angle, dividing it into two equal parts. As a result, any point on this line will be equidistant from the endpoints of the segment.
14.
The _____________ distance from a point to a line is measured along the perpendicular from the point to the line.
Correct Answer
C. Shortest
Explanation
The shortest distance from a point to a line is measured along the perpendicular from the point to the line. This means that the distance is the shortest possible distance between the point and the line, as it is measured in a straight line perpendicular to the line.
15.
What is the definition of an altitude?
16.
What two ways can you make constructions?
Correct Answer
D. Both a and b
Explanation
Both a and b are correct because you can make constructions using patty paper, which is a transparent paper that can be folded and manipulated, as well as using a compass and straightedge, which are traditional tools used in geometry to create precise geometric shapes and constructions. Additionally, ruler and protractor (option c) is incorrect because a ruler and protractor alone cannot be used to create constructions without the aid of a compass or straightedge.
17.
Is the converse of the Vertical Angles Conjecture true or false?
Correct Answer
B. False
Explanation
The converse of the Vertical Angles Conjecture states that if two angles are not vertical angles, then they are not congruent. This statement is false because there are cases where two angles are not vertical angles but still congruent, such as when they are corresponding angles formed by a transversal intersecting two parallel lines. Therefore, the converse of the Vertical Angles Conjecture is false.