Questions and Answers
What is the sum of the measures of the three interior angles of a triangle?
180 degrees
What is an exterior angle?
An angle that is supplementary and adjacent to the interior angle.
The measure of the exterior angle of a triangle is equal to...
The sum of the remote interior angles.
What is a segment joining two midpoints of two sides of a triangle?
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If two pairs of angles of two triangles are congruent, what can be said about the third pair?
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What do we call the theorem that describes certain conditions for triangle congruence?
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What is another way to prove a triangle congruent?
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Match the number of sides to the corresponding polygon names:
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In formulas involving polygons, what does 'n' represent?
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What is the formula for finding the sum of interior angle measures?
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What is the sum of exterior angles on every polygon?
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What is the diagonal formula?
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What is a regular polygon?
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To find the measure of each exterior angle, what formula should be used?
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To find the measure of each interior angle, what formula should be used?
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What is the Pythagorean theorem?
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Study Notes
Interior Angles of a Triangle
- The sum of the three interior angles in a triangle is 180 degrees.
Exterior Angles
- An exterior angle is supplementary to its adjacent interior angle.
- The measure of an exterior angle equals the sum of the remote interior angles of a triangle.
Midsegment of a Triangle
- A segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
Triangle Angle Congruence
- If two pairs of angles in two triangles are congruent, the third pair of angles must also be congruent.
- This principle is known as the no choice theorem.
Triangle Congruence Criteria
- A triangle can be proven congruent through Angle-Angle-Side (AAS), involving two angles and a non-included side.
Polygon Sides and Names
- Different polygons based on their number of sides:
- 3 sides: Triangle
- 4 sides: Quadrilateral
- 5 sides: Pentagon
- 6 sides: Hexagon
- 7 sides: Heptagon
- 8 sides: Octagon
- 9 sides: Nonagon
- 10 sides: Decagon
- 12 sides: Dodecagon
- 15 sides: Pentadecagon
- 20 sides: Icosagon
Polygon Formulas
- In formulas involving polygons, "n" represents the number of sides.
- The formula to find the sum of interior angle measures is (n-2) × 180 degrees.
- The sum of the exterior angles for any polygon is always 360 degrees.
- The diagonal formula for polygons is n(n-3)/2.
Regular Polygons
- A regular polygon is defined as being both equilateral (all sides equal) and equiangular (all angles equal).
Angle Measures
- To find the measure of each exterior angle of a polygon, use the formula 360/n.
- To find the measure of each interior angle, the formula is 180 - (360/n).
Pythagorean Theorem
- The Pythagorean theorem states that a² + b² = c², where "c" represents the hypotenuse in a right triangle.
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Description
Test your knowledge on polygons with this quiz from Geometry Chapter 7. It covers key concepts such as the interior and exterior angles of triangles and properties of geometric figures. Enhance your understanding and retention of geometry fundamentals.
