Podcast
Questions and Answers
In triangle ABC, $AB = 5$ cm, and $BC = 8$ cm. According to the Triangle Inequality Theorem, which of the following could be a possible length for side AC?
In triangle ABC, $AB = 5$ cm, and $BC = 8$ cm. According to the Triangle Inequality Theorem, which of the following could be a possible length for side AC?
- 2 cm
- 14 cm
- 12 cm (correct)
- 3 cm
Given a triangle where one exterior angle measures 120°, which of the following statements must be true according to the Exterior Angle Inequality Theorem?
Given a triangle where one exterior angle measures 120°, which of the following statements must be true according to the Exterior Angle Inequality Theorem?
- One of the remote interior angles is greater than 120°.
- One of the remote interior angles is equal to 60°.
- Both remote interior angles are less than 120°. (correct)
- Both remote interior angles are greater than 120°.
Two triangles, $\triangle ABC$ and $\triangle XYZ$, have $AB = XY$ and $BC = YZ$. If $\angle B > \angle Y$, which theorem justifies the conclusion that $AC > XZ$?
Two triangles, $\triangle ABC$ and $\triangle XYZ$, have $AB = XY$ and $BC = YZ$. If $\angle B > \angle Y$, which theorem justifies the conclusion that $AC > XZ$?
- Converse of the Hinge Theorem
- Exterior Angle Inequality Theorem
- Triangle Inequality Theorem
- Hinge Theorem (correct)
In $\triangle PQR$, if $PQ = 10$ cm and $PR = 8$ cm, and $\angle R = 60°$, which of the following statements must be true?
In $\triangle PQR$, if $PQ = 10$ cm and $PR = 8$ cm, and $\angle R = 60°$, which of the following statements must be true?
Line $l$ and line $m$ are parallel and cut by a transversal $t$. If one of the interior angles on the same side of the transversal is 110°, what is the measure of the other interior angle on the same side?
Line $l$ and line $m$ are parallel and cut by a transversal $t$. If one of the interior angles on the same side of the transversal is 110°, what is the measure of the other interior angle on the same side?
Which condition is sufficient to prove that two lines cut by a transversal are parallel?
Which condition is sufficient to prove that two lines cut by a transversal are parallel?
Line $p$ has a slope of 2. Which of the following slopes would indicate a line $q$ that is perpendicular to line $p$?
Line $p$ has a slope of 2. Which of the following slopes would indicate a line $q$ that is perpendicular to line $p$?
A bag contains 5 red balls and 3 blue balls. If you draw one ball at random, what is the sample space for this experiment?
A bag contains 5 red balls and 3 blue balls. If you draw one ball at random, what is the sample space for this experiment?
How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is allowed?
How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is allowed?
A fair six-sided die is rolled. What is the theoretical probability of rolling an even number?
A fair six-sided die is rolled. What is the theoretical probability of rolling an even number?
Flashcards
Triangle Inequality Theorem
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Exterior Angle Inequality Theorem
Exterior Angle Inequality Theorem
An exterior angle of a triangle is greater than either of the non-adjacent interior angles.
Hinge Theorem and Converse
Hinge Theorem and Converse
If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Converse: If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
Side-Angle Relationship
Side-Angle Relationship
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Angle-Side Relationship
Angle-Side Relationship
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Parallel Lines and Transversals
Parallel Lines and Transversals
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Proving Parallel Lines
Proving Parallel Lines
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Probability Concepts
Probability Concepts
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Counting Possible Outcomes
Counting Possible Outcomes
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Probability of a Simple Event
Probability of a Simple Event
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Study Notes
- Tomorrow is the unit test.
- Review all lessons thoroughly.
- The 4th Quarter Unit Test covers these topics:
Theorems on Triangle Inequalities:
- Triangle Inequality Theorem
- Exterior Inequality Theorem
- The Hinge Theorem and its Converse
- Angle-Side Relationship
- Side-Angle Relationship
Parallel Lines and Transversals
- Properties of Parallel Lines Cut by a Transversal
- Proving Parallel Lines Cut by a Transversal
- Conditions for Parallelism and Perpendicularity
Probability Concepts
- Illustrating Experiments, Outcomes, Sample Space, and Events
- Four Different Methods for Counting Possible Outcomes
- Finding the Probability of a Simple Event (Experimental and Theoretical Probability)
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