Podcast
Questions and Answers
The measure of an ____________ angle of a triangle is greater than the measure of either remote _______________ angle.
The measure of an ____________ angle of a triangle is greater than the measure of either remote _______________ angle.
exterior, interior
If one side of a triangle is __________ than a second side, then the _________ opposite the first side is larger than the angle opposite the second side.
If one side of a triangle is __________ than a second side, then the _________ opposite the first side is larger than the angle opposite the second side.
larger, angle
If one angle of a triangle is __________ than a second angle, then the ____________ opposite the first angle is larger than the side opposite the second angle.
If one angle of a triangle is __________ than a second angle, then the ____________ opposite the first angle is larger than the side opposite the second angle.
greater, side
The sum of the lengths of any two ____________ of a _____________ is greater than the length of the third side.
The sum of the lengths of any two ____________ of a _____________ is greater than the length of the third side.
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If two sides of one ____________ are congruent to two sides of another _____________ BUT the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is _____________ than the third side of the second triangle.
If two sides of one ____________ are congruent to two sides of another _____________ BUT the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is _____________ than the third side of the second triangle.
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If two sides of one triangle are ______________ to two sides of another triangle, BUT the third side of the first is _______________ than the third side of the second, then the included angle of the first is larger than the included angle of the second triangle.
If two sides of one triangle are ______________ to two sides of another triangle, BUT the third side of the first is _______________ than the third side of the second, then the included angle of the first is larger than the included angle of the second triangle.
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What is the inverse in logical terms?
What is the inverse in logical terms?
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What is the converse in logical terms?
What is the converse in logical terms?
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What is the conditional in logical terms?
What is the conditional in logical terms?
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What is the contrapositive in logical terms?
What is the contrapositive in logical terms?
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Study Notes
Exterior Angle Inequality Theorem
- An exterior angle of a triangle is greater than either of the remote interior angles.
Theorem 6-2
- If one side of a triangle is larger than another side, the angle opposite the larger side is also larger than the angle opposite the smaller side.
Theorem 6-3
- If one angle in a triangle is greater than another angle, the side opposite the greater angle is larger than the side opposite the smaller angle.
Theorem 6-4
- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
SAS Inequality Theorem
- If two sides of one triangle are congruent to two sides of another triangle and the included angle in the first triangle is larger, then the third side of the first triangle is greater than that of the second triangle.
SSS Inequality Theorem
- If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is larger, then the included angle opposite the larger side in the first triangle is also larger.
Logical Statements
- Inverse: If not p, then not q.
- Converse: If q, then p.
- Conditional: If p, then q.
- Contrapositive: If not q, then not p.
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Description
Test your knowledge of Geometry concepts with our Chapter 6 Practice Test flashcards. This quiz covers essential theorems and properties, including the Exterior Angle Inequality Theorem. Perfect for mastering triangle properties and their applications.
