Question

16
the shaded region represents-
o a line segment
o an angle
o part of a plane
o a triangle
17
which is a true statement about angles 1 and 2 shown below?
o both angles are acute.
o ∠1 is complementary to ∠2.
o ∠1 is supplementary to ∠2.
o both angles are obtuse.
18
by inductive reasoning, the number of digits in the product of 3 two - digit numbers is
o 5
o 4, 5, or 6
o 4 or 6
o 4
19
point b lies between points a and c, and all three points lie on line ac. which of
the following is not true?
o point c lies on ray ab.
o point c lies on line ab.
o point b lies on segment ac.
o point a lies on ray bc.
20
the asa congruency axiom states that two triangles are congruent if:
o two sides and the excluded angle of one triangle are equal to two sides and
the excluded angle of the other triangle.
o they are right triangles and the hypotenuse and one side of one triangle are
equal to the hypotenuse and one side of the other triangle.
o two sides and the contained angle of one triangle are equal to two sides and
the contained angle of the other triangle.
o two angles and the contained side of one triangle are equal to two angles
and the contained angle of the other triangle.

Explanation:

1. Question 16:

• Analysis:
• A line segment is a part of a line with two endpoints. An angle is formed by two rays with a common endpoint. A triangle is a polygon with three sides. A plane is a flat, two - dimensional surface. The shaded region in the 3 - D figure (a rectangular prism) is a flat surface, which is part of a plane.
• Answer: part of a plane

1. Question 17:

• Analysis:
• Acute angles are angles less than \(90^{\circ}\), obtuse angles are angles greater than \(90^{\circ}\) but less than \(180^{\circ}\). Complementary angles add up to \(90^{\circ}\), and supplementary angles add up to \(180^{\circ}\). Since \(\angle1+\angle2 = 180^{\circ}\) (they form a linear pair), \(\angle1\) is supplementary to \(\angle2\).
• Answer: \(\angle1\) is supplementary to \(\angle2\)

1. Question 18:

• Analysis:
• Let's take examples. The smallest two - digit numbers: \(10\times10\times10=1000\) (4 digits). The largest two - digit numbers: \(99\times99\times99=(100 - 1)\times(100 - 1)\times(100 - 1)=(10000-200 + 1)\times(100 - 1)=(9801)\times(100 - 1)=980100-9801=970299\) (6 digits). Also, \(20\times20\times20 = 8000\) (4 digits), \(30\times30\times30=27000\) (5 digits).
• Answer: 4, 5, or 6

1. Question 19:

• Analysis:
• A ray \(AB\) has endpoint \(A\) and extends through \(B\). If \(B\) is between \(A\) and \(C\) on line \(AC\), point \(C\) does not lie on ray \(AB\) (ray \(AB\) goes from \(A\) through \(B\) and not beyond \(B\) in the direction away from \(A\)). Point \(C\) lies on line \(AB\) (since \(A\), \(B\), \(C\) are collinear). Point \(B\) lies on segment \(AC\) (by the given condition). Point \(A\) lies on ray \(BC\) (ray \(BC\) has endpoint \(B\) and extends through \(C\), and \(A\) is on the line \(BC\) on the opposite side of \(B\) from \(C\)).
• Answer: Point \(C\) lies on ray \(AB\)

1. Question 20:

• Analysis:
• The ASA (Angle - Side - Angle) congruency axiom states that two triangles are congruent if two angles and the included (contained) side of one triangle are equal to two angles and the included (contained) side of the other triangle.
• Answer: two angles and the contained side of one triangle are equal to two angles and the contained angle of the other triangle.

Answer:

1. Question 16:

• Analysis:
• A line segment is a part of a line with two endpoints. An angle is formed by two rays with a common endpoint. A triangle is a polygon with three sides. A plane is a flat, two - dimensional surface. The shaded region in the 3 - D figure (a rectangular prism) is a flat surface, which is part of a plane.
• Answer: part of a plane

1. Question 17:

• Analysis:
• Acute angles are angles less than \(90^{\circ}\), obtuse angles are angles greater than \(90^{\circ}\) but less than \(180^{\circ}\). Complementary angles add up to \(90^{\circ}\), and supplementary angles add up to \(180^{\circ}\). Since \(\angle1+\angle2 = 180^{\circ}\) (they form a linear pair), \(\angle1\) is supplementary to \(\angle2\).
• Answer: \(\angle1\) is supplementary to \(\angle2\)

1. Question 18:

• Analysis:
• Let's take examples. The smallest two - digit numbers: \(10\times10\times10=1000\) (4 digits). The largest two - digit numbers: \(99\times99\times99=(100 - 1)\times(100 - 1)\times(100 - 1)=(10000-200 + 1)\times(100 - 1)=(9801)\times(100 - 1)=980100-9801=970299\) (6 digits). Also, \(20\times20\times20 = 8000\) (4 digits), \(30\times30\times30=27000\) (5 digits).
• Answer: 4, 5, or 6

1. Question 19:

• Analysis:
• A ray \(AB\) has endpoint \(A\) and extends through \(B\). If \(B\) is between \(A\) and \(C\) on line \(AC\), point \(C\) does not lie on ray \(AB\) (ray \(AB\) goes from \(A\) through \(B\) and not beyond \(B\) in the direction away from \(A\)). Point \(C\) lies on line \(AB\) (since \(A\), \(B\), \(C\) are collinear). Point \(B\) lies on segment \(AC\) (by the given condition). Point \(A\) lies on ray \(BC\) (ray \(BC\) has endpoint \(B\) and extends through \(C\), and \(A\) is on the line \(BC\) on the opposite side of \(B\) from \(C\)).
• Answer: Point \(C\) lies on ray \(AB\)

1. Question 20:

• Analysis:
• The ASA (Angle - Side - Angle) congruency axiom states that two triangles are congruent if two angles and the included (contained) side of one triangle are equal to two angles and the included (contained) side of the other triangle.
• Answer: two angles and the contained side of one triangle are equal to two angles and the contained angle of the other triangle.