Title: prueba
Course: 2025 Probabilidad y Estadística

Q: When using induction, one draws a conclusion based upon numerous examples or test results.
- True
- False
A: True

Q: Because it has rained the past 4 days, a person's intuition can be used to conclude that it will definitely rain again tomorrow.
- True
- False
A: False

Q: Where A = {1,2,3,4,5} and B = {2,4,6,8,10}, it follows that A Ç B = {1,2,3,4,5,6,8,10}.
- True
- False
A: False

Q: [Image]

If AB = 7.4 and BC = 13.7, then AC = 20.1.
- True
- False
A: False

Q: Points A, B, and C are said to be collinear if they lie on a line.
- True
- False
A: True

Q: A postulate is accepted without proof while a theorem is a statement that must be proved.
- True
- False
A: True

Q: An angle is the union of two rays that have a common endpoint.
- True
- False
A: True

Q: [Image]

According to the Angle-Addition Postulate, m [Image] [Image] m [Image] = m [Image].
- True
- False
A: True

Q: Where x is the measure of an angle and 0° < x < 90°, the angle is an obtuse angle.
- True
- False
A: False

Q: If ray BD bisects [Image], then [Image] [Image] [Image].
- True
- False
A: True

Q: If B is the midpoint of line segment AC and AB = 3.6, then AC = 7.2.
- True
- False
A: True

Q: If [Image] bisects [Image] and m [Image] = 4x [Image] 20, then m [Image] = 2x [Image] 20.
- True
- False
A: False

Q: [Image]

In the figure, [Image] and [Image] are known as vertical angles.
- True
- False
A: True

Q: If [Image] and [Image] are vertical angles with m [Image] = 2x [Image] 5 and m [Image] = 39, then x = 17.
- True
- False
A: False

Q: [Image]

With [Image] [Image] [Image] and point G in the interior of [Image], [Image] and [Image] are complementary.
- True
- False
A: True

Q: If [Image] and [Image] are complementary, then each of these angles 1 and 2 is acute.
- True
- False
A: True

Q: The relation between lines, "is perpendicular to," has a transitive property.
- True
- False
A: False

Q: If two rays are opposite rays, then their union is a straight line.
- True
- False
A: True

Q: [Image] can also be called [Image].
- True
- False
A: False

Q: When lines [Image] and m intersect at point P, it follows that  [Image] [Image] m = P.
- True
- False
A: True

Q: Which is not a method of reasoning used in geometry?
- construction
- induction
- intuition
- deduction
A: construction

Q: Given that A = {1,2,3,4,5} and B = {2,4,6,8}, it follows that:
- A [Image] B = {2,4}
- A ÇB = {2,4}
- A [Image] B
- B [Image]A
A: A ÇB = {2,4}

Q: Points A, B, C, and D are collinear so that A-B-C-D. If AB = 7, AC = 11, and CD = 6, then AD equals:
- 12
- 15
- 17
- 24
A: 17

Q: For a construction problem, which instrument could you use?
- calculator
- protractor
- tape measure
- compass
A: compass

Q: Point M is the midpoint of [Image]. If AM = 12 and AB = 5x [Image] 6, find x:
- x = 3.6
- x = 6
- x = 7.2
- None of These
A: x = 6

Q: In geometry, what is a postulate?
- statement that defines a term
- statement that must be proved
- a type of geometric figure
- None of These
A: None of These

Q: Consider the definition: An isosceles triangle is a triangle that has two congruent sides. Which result must follow from the definition?
- If [Image] is isosceles, then it has two congruent angles.
- If [Image] [Image] [Image] in [Image], then [Image] is an isosceles triangle.
- If [Image] has two congruent sides, then [Image] has two congruent angles.
- None of These
A: If [Image] [Image] [Image] in [Image], then [Image] is an isosceles triangle.
If right: The definition has a reversible characteristic.
If wrong: The definition has a reversible characteristic.

Q: Which property justifies this conclusion?
If X is a point on [Image] and R-X-S, then RX [Image] XS = RS.
- Segment-Addition Postulate
- Line-Addition Postulate
- Ruler Postulate
- None of These
A: Segment-Addition Postulate

Q: Given lines [Image] and m with [Image] [Image] m, it follows that:
- [Image] [Image] m = [Image]
- [Image] [Image] m = [Image]
- [Image] [Image] m
- None of These
A: [Image] [Image] m = [Image]

Q: If m [Image] = x and 90° < x < 180°, then [Image] is a(n):
- acute angle
- right angle
- obtuse angle
- straight angle
A: obtuse angle

Q: [Image]

If m [Image] = 2x [Image] 17, m [Image] = 4(x [Image] 3), and m [Image] = 8x [Image] 12, find x.
- x = 8
- x = 8.25
- x = 8.5
- x = 8.75
A: x = 8.5

Q: [Image] and [Image] are adjacent angles. Where m [Image] = x and m [Image] = y, we have x [Image] y = 57 and x [Image] y = 23. Find m [Image].
- 33°
- 36°
- 38°
- 40°
A: 40°

Q: Given that 2x [Image] 3 = 17, which operation leads to the conclusion that 2x = 14?
- adding 3 to each side of the equation
- adding [Image]3 to each side of the equation
- subtracting [Image] from each side of the equation
- None of These
A: adding [Image]3 to each side of the equation

Q: If M is the midpoint of [Image], then it can be proved that:
- N is also the midpoint of [Image].
- AM = [Image](AB)
- AM = [Image](AB)
- None of These
A: AM = [Image](AB)

Q: [Image]

If [Image] [Image] [Image], then it can be proved that:
- [Image] [Image] [Image]
- [Image] is a right angle
- [Image] bisects [Image]
- None of These
A: [Image] [Image] [Image]

Q: Consider a set of lines. Which is a property of the relation "is perpendicular to" for lines?
- Reflexive
- Symmetric
- Transitive
- None of These
A: Symmetric

Q: For two intersecting lines, [Image] and [Image] are a pair of vertical angles formed. Given that
m [Image] = [Image] [Image] 7 and m [Image] = [Image] [Image] 5, find the value of x.
- x = 12
- x = 24
- x = 36
- x = 72
A: x = 72

Q: Considering the definitions and postulates of geometry, which of the following is a correct statement?
- An angle has more than one angle-bisector.
- A line segment has two midpoints.
- A line segment has two endpoints.
- A plane contains exactly three noncollinear points.
A: A line segment has two endpoints.

Q: [Image]

Given A-B-C and m [Image] = x [Image] y [Image] 17 while m [Image] = 2x [Image] 3y [Image] 5, it follows that:
- 3x [Image] 2y = 78
- 3x [Image] 2y = 158
- x [Image] y [Image] 17 = 2x [Image] 3y [Image] 5
- None of These
A: 3x [Image] 2y = 158

Q: Given that 2(x [Image] 4) [Image] 9 = 17, you can prove that:
- x = 2
- x = 15
- x = 16
- None of These
A: None of These

Q: Where P and Q are statements, the compound statement "P or Q" is known as a(n):
A: disjunction

Q: For sets R and T, it follows that R [Image] (R [Image] T) is the same as:
A: R

Q: Complete the following implication with hypothesis "2 [Image] 3 = 5."
If 2 + 3 = 5, then 2a [Image] 3a = ?:
A: 5a.

Q: The instrument used to construct circles and arcs is the:
A: compass

Q: If ray BD bisects [Image], then m [Image] = [Image](?)
A: m

Q: A property of geometry that is accepted as true without proof is a(n):
A: postulate

Q: If [Image] and [Image] are supplementary and [Image] [Image] [Image], then [Image] must be a(n):
A: right angle

Q: If B is the midpoint of [Image] and BC = 2.78 inches, then AC measures:
A: 5.56 inches

Q: If R-S-T on line RT and RS = 2x [Image] 5 while RT = 7x [Image] 3, then ST measures:
A: 5x

Q: If two planes intersect, they intersect in a(n):
A: line

Q: [Image]

If two lines intersect, any two adjacent angles formed are:
A: supplementary

Q: [Image]

If X is the midpoint of [Image] and X-V-T on [Image], RX = 2x [Image] 1, XS = 3x [Image] 5, TX = 3x [Image] 4, and
XV = 2x [Image] 3, find the length of [Image].
A: 29

Q: [Image]

If m [Image] = 34° and m [Image] = 46°, then m [Image] equals:
A: 80°

Q: [Image]

If [Image] (not shown) bisects [Image] and m [Image] = 37°, then m [Image] equals:
A: 106°

Q: Complete the conclusion from the following true statements:
  (1) If two triangles are similar, then they have the same shape.
  (2) Triangle ABC and triangle DEF are similar.
  (C) Triangle ABC and triangle DEF have ? ? ?
A: the same shape.

Q: [Image] is separated into smaller angles by [Image] and [Image], rays in the interior of [Image].
If  m [Image] = x [Image] y, m [Image] = y [Image] 2, and m [Image] = 3y [Image] x, then m [Image] equals:
A: 5y

Q: If two angles are supplementary and also congruent, then each of these angles is a(n):
A: right angle

Q: [Image]

In the figure, the exterior sides of the adjacent angles ( [Image] and [Image]) form a larger angle ( [Image]). If m [Image] = 49° and m [Image] = 58°, what type of angle is [Image]?
A: obtuse angle

Q: [Image]

In the figure, the exterior sides of the adjacent angles ( [Image] and [Image]) form perpendicular rays. How are these angles related?
A: They are complementary.