Mathematics 8 4th Quarter Exam Review

In $\triangle ABC$, if $AB = 5$ and $BC = 8$, which of the following could be the length of $AC$ according to the Triangle Inequality Theorem?

Given $\triangle PQR$, where $PQ = 10$, $QR = 12$, and $RP = 15$. Which angle is the largest?

If an exterior angle of a triangle measures $120^\circ$, which of the following statements must be true?

In $\triangle XYZ$, $\angle X = 50^\circ$ and $\angle Y = 70^\circ$. Which side is the longest?

Given two triangles $\triangle ABC$ and $\triangle DEF$ where $AB = DE$, $BC = EF$, and $\angle B > \angle E$, what can be concluded about the relationship between $AC$ and $DF$ according to the Hinge Theorem?

If $AC = DF$, $AB = DE$, and $BC > EF$ in triangles $\triangle ABC$ and $\triangle DEF$, which of the following statements is true according to the Converse of the Hinge Theorem?

To prove that the base angles of an isosceles triangle are congruent, which of the following auxiliary lines is typically constructed?

In a proof, which justification supports the statement that $AB + BC > AC$ for any three non-collinear points A, B, and C?

If two parallel lines are intersected by a transversal, which pair of angles are supplementary?

Given that line $l$ is parallel to line $m$, and both are intersected by transversal $t$. If one of the angles formed is $60^\circ$, what is the measure of its corresponding angle?

To prove that alternate exterior angles formed by parallel lines cut by a transversal are congruent, which theorem is most directly applied after establishing that corresponding angles are congruent?

To prove that same-side interior angles are supplementary, which of the following angle relationships is typically used?

Which of the following describes a sample space in an experiment?

A bag contains 3 red marbles and 2 blue marbles. What is the sample space when selecting one marble from the bag?

What is the definition of an 'event' in probability?

When rolling a fair six-sided die, what is the event of rolling an even number?

Which of the following counting methods is best suited for determining the number of ways to arrange books on a shelf, where the order matters?

How many ways can you choose 3 students out of a group of 5 for a committee, if the order of selection does not matter?

A restaurant offers 4 appetizers, 5 main courses, and 3 desserts. How many different meals, consisting of one appetizer, one main course, and one dessert, can be ordered?

A coin is flipped three times. What is the probability of getting exactly two heads?

In $\triangle ABC$, $AB = 7$, $BC = 9$, and $AC = 11$. Which of the following is true about the angles of the triangle?

In $\triangle XYZ$, $XY = 6$, $YZ = 8$, and $XZ = 10$. Which angle is the smallest?

If an exterior angle of a triangle measures $130^\circ$, what can be concluded about the two remote interior angles?

Given two triangles $\triangle ABC$ and $\triangle DEF$ where $AB = DE$, $BC = EF$, and $AC < DF$, what can be concluded about the relationship between $\angle B$ and $\angle E$?

In proving the Triangle Inequality Theorem, why is it important to consider the shortest distance between two points?

When proving the properties of parallel lines cut by a transversal, which property is often used as a starting point?

Given line $m$ is parallel to line $n$, and both are intersected by transversal $t$. If one of the interior angles on the same side of the transversal is $110^\circ$, what is the measure of the other interior angle on the same side?

What makes an experiment a fair experiment?

A spinner has four equally sized sections colored red, blue, green, and yellow. What is the sample space for spinning the spinner once?

What is the difference between an outcome and an event?

A bag contains 5 yellow candies, 3 green candies and 2 red candies. What is the probability of drawing either a green or red candy?

Which counting method is used to find the number of possible outcomes when selecting a president, a vice president, and a treasurer from a group of 10 people?

How many different committees of 4 people can be formed from a group of 8 people?

A bakery sells 6 types of donuts. If you want to buy 3 donuts, how many different selections can you make?

A bag contains 4 red balls and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that the first ball is red and the second ball is blue?