WorksheetsMath 8 Triangle Inequalities and Probability
Total questions: 45
Worksheet time: 23mins
Which theorem states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side?
Triangle Inequality Theorem
Angle-Side Relationship Theorem
Exterior Angle Inequality Theorem
Hinge Theorem or SAS Inequality Theorem
In Triangle Inequality Theorem, which of the following describes the relationship of the sum of its two sides to its third length?
greater than
greater than or equal to
less than
less than or equal to
Which of the following theorems deals with the two triangles whose two corresponding sides are congruent and whose included angle are unequal?
SAS Inequality Theorem
Angle-Side Relationship Theorem
SSS Inequality Theorem
Exterior Angle Inequality Theorem
Which of the following could NOT be used as the length of the sides of a triangle?
3, 3, 3
4, 5, 10
5, 7, 9
10, 20, 20
Given the figure at the right, which of the following angles is an exterior angle of ∆ DER?
∠3
∠4
∠2
∠1
In ∆ 𝑁𝐸𝑇, 𝑁𝐸= 14 cm, 𝐸𝑇̅̅̅̅ = 15 cm, 𝑁𝑇̅̅̅̅ = 16 cm. What is the correct order of the angles when arranged from least to greatest?
∠E, ∠N, ∠T
∠E, ∠T, ∠N
∠T, ∠E, ∠N
∠T, ∠N, ∠E
Carlos concluded that the longest side in 𝛥𝑀𝐴𝑃 is 𝐴𝑃̅̅̅̅ after finding that the angle opposite to 𝐴𝑃̅̅̅̅ is the largest angle. What theorem did Carlos use to make such conclusion?
Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)
Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)
Hinge Theorem or SAS Triangle Inequality Theorem
Converse of Hinge Theorem or SSS Triangle Inequality Theorem
What is the largest angle?
∠𝐸
∠𝑁
∠𝑃
Cannot be determined.
What is the smallest angle?
∠𝐸
∠𝑁
∠𝑃
Cannot be determined.
Which property of equality is defined by the statement "For all real numbers 𝑝, 𝑝 = 𝑝"?
Reflexive Property
Transitive property
Symmetric Property
Substitution Property
Which of the following theorems states that "base angles of isosceles triangles are congruent"?
Linear Pair Theorem
Exterior Angle Theorem
Vertical Angles Theorem
Isosceles Triangle Theorem
Ryan is analyzing the pair of triangles in the figure below. Which of the following is the correct observation?
𝑅𝐴̅̅̅̅ ≅ 𝐶𝐸̅̅̅̅
|𝐶𝐸| > |𝑅𝐸|
𝑚∠𝑅𝐸𝐴 < 𝑚∠𝐶𝐸𝐴
𝑚∠𝑅𝐸𝐴 > 𝑚∠𝐶𝐸𝐴
What can be said about the alternate interior angles if two parallel lines are cut by a transversal?
complementary
congruent
parallel
perpendicular
What do you call those two coplanar lines that do not intersect?
congruent
parallel
perpendicular
supplementary
If 𝑚∠𝑎 = 99˚ , what is the measure of ∠𝑑?
45˚
81˚
90˚
99˚
Rona was asked by her teacher to find the value of 𝒚 given that 𝑚∠𝑎 = 6𝑦 and 𝑚∠𝑐 = 13𝑦 − 100. She wrote her computation in this way: Did she arrive at the correct answer?
Yes. Common variables must be combined.
No. The equation must be (6𝑦) = (13𝑦 − 10).
No. Multiplying both sides of the equation by 1 19 is not equal to 𝑦 = 10.
Yes. The equation she formulated is correct since ∠𝑎 and ∠𝑐 are supplementary angles.
Which of the following statements above is/are NOT true about two parallel lines?
I only
I and III only
III only
II and IV only
Which is/are true about perpendicular lines?
II only
II and IV only
I and IV only
II and III only
Anna was asked by her teacher to find the perimeter of the floor of their classroom with a length of 18 m and a width of 12 m. Is Anna correct when she got a perimeter of 60 m?
No, the perimeter of the floor of the classroom should be 216 m.
Yes, since the floor of the classroom is a quadrilateral.
Yes, since the floor of the classroom is a rectangle.
No, the perimeter should be 30 m.
Given the parallelogram FARM, if m ˂M = 42◦, what is the measure of ˂F?
138°
128°
48°
42°
What do you call the set of all possible outcomes of an experiment?
Event
Experiment
Sample Point
Sample Space
How many aces are there in a standard deck of 52 playing cards?
4
6
10
13
If you roll two dice once, how many possible outcomes are there?
8
16
26
36
How many aces are there in a standard deck of 52 playing cards?
4
6
10
13
If you roll two dice once, how many possible outcomes are there?
8
16
26
36
Arlene got coins from her pocket which accidentally rolled on the floor. If there were 4 possible outcomes, how many coins fell on the floor?
1
2
3
4
Which of the following is the way of finding the total number of outcomes of an experiment without enumerating those outcomes?
Tabular
Tree diagram
Systematic listing
Fundamental Counting Principle
What do you call the method of determining the total number of outcomes of an experiment with at least two events where every possible outcome of the first event is paired with every possible outcome of each succeeding event using lines?
Tabular
Tree diagram
Systematic listing
Fundamental Counting Principle
A canteen sells three types of snack foods and two types of homemade juices. Grace can choose one snack food and one juice. How do you determine the total number of possible choices that Grace have for her snacks?
2 x 2
3 x 2
3 x 3
22 x 32
Juanito got coins from his pocket which accidentally rolled on the floor. He learned from his lesson in probability that with this number of coins tossed once, the number of possible outcomes is 8. How many coins fell on the floor?
8
4
3
1
Healthcare workers treating patients infected with Coronavirus Disease 2019 (COVID-19) are at risk of infection, so they use personal protective equipment (PPE) to shield themselves from infection. PPE includes gown or overalls, face mask, pair of gloves, and goggles. A healthcare worker in Philippine General Hospital has eight overalls, ten face masks, six pairs of gloves, and five goggles. In this case, which of the following counting techniques is best to use in determining the total number of possible ways a healthcare worker can wear his PPE?
table
tree diagram
systematic listing
fundamental counting principle
What do you call an event that can happen in a unique way?
Complementary Event
Dependent Event
Independent Event
Simple Event
The local weather forecaster said that there is 70% chance of rain tomorrow. What is the probability that it will not rain tomorrow?
0.3
0.7
30
70
Rica 's chance of winning a game is 23. What is the likelihood that Rica will win the game?
certain
impossible
likely
unlikely
The numbers 4 to 10 are written on separate pieces of paper, folded and placed in a box. One number (piece of paper) is drawn from this box. What is the probability that the number chosen is a composite number?
110
15
12
57
There are 7 blue marbles, 12 red marbles, 15 green marble, and 2 black marbles in a bag. Suppose you select 1 marble at random, what is the probability that you get a red marble?
13
118
718
14
Which of the following is true about theoretical probability?
It is the relative approximation of probability of an event.
Experiment needs to be done to get the probability of an event.
It is the probability of the event that a person is expecting to happen.
It is an approach that bases the probability on the possible chances of an event to happen.
Which of the following illustrates experimental probability?
In rolling a die once, the probability of getting a 6 is 1/6.
In flipping a coin once, the probability of getting a head is ½.
The probability of drawing a non-spade card from a deck of 52 cards is 3/4.
In tossing a coin 500 times, head turned up 235 times, then the probability of the tail turning up is 265/500
Consider the situation 'A coin is flipped four times.'. How many possible outcomes are there?
4
8
16
32
How does experimental probability differ from theoretical probability?
There is no difference between experimental probability and theoretical probability of an event.
Experimental probability is observation-based probability while theoretical probability is expected probability.
Experimental probability is based on the expected outcome while theoretical probability is based on the observations in the experiment.
Experimental probability is the ratio of the number of favorable outcomes to the total number of possible outcomes while theoretical probability is the ratio of the number of times the event occurred to the total number of trials.
You got coins from your pocket which accidentally fell on the floor. If there were 8 possible outcomes, how many coins fell on the floor?
3
4
8
16
Two dice are rolled, what is the probability that a 3 turns up on the first die and a divisor of nine on the second die?
136
118
112
29
What is the sum of the interior angles of a triangle?
270 degrees
180 degrees
90 degrees
360 degrees
In a right triangle, if one angle measures 30 degrees, what is the measure of the other non-right angle?
90 degrees
60 degrees
30 degrees
45 degrees
What is the probability of drawing a heart from a standard deck of 52 playing cards?
1/4
1/52
1/2
1/13
