Questions and Answers
Find the measure of the missing angle: 166°
14°
How many sides does a heptagon have?
7
What is a five-sided figure called?
pentagon
How many sides does a nonagon have?
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What do you call a 6-sided figure?
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Identify the concave polygon figure.
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What does it mean to be a regular polygon?
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ABCD is a parallelogram, if m∠ABC=96°, what is m∠ADC?
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ABCD is a parallelogram, if m∠ABC=96°, what is m∠BAD?
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Find the value of 'z' in the parallelogram.
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In parallelogram LMNO, LM=7x - 4 and NO = 4x + 11. Find the value of x.
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The diagonals of a parallelogram always _______.
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Find the measure of the mid segment for the following trapezoid.
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If all four sides of a quadrilateral are congruent, the quadrilateral is a _______.
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What does it mean for a trapezoid to be isosceles?
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Which type of quadrilateral has no parallel sides?
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If ABCD is an isosceles trapezoid, find the length of BD.
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If ABCD is an isosceles trapezoid, find the m∠ABC.
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For kite ABCD, AC = 30, BD = 22, what is the length of DM?
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For kite ABCD, if m∠BAD = 75° and m∠BCD = 125°, find m∠ADC.
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What are some properties for an isosceles trapezoid?
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What would be the sum of the interior angles for a 17-sided polygon?
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What would be the measure of an interior angle for a regular decagon?
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∠1 and ∠2 are supplementary. ∠2 and ∠3 are vertical angles. If m∠1 = 43°, find m∠3.
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Find the m∠Y.
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Study Notes
Quadrilaterals and Polygons
- A heptagon has 7 sides.
- A five-sided figure is called a pentagon.
- A nonagon contains 9 sides.
- A hexagon is defined as a 6-sided figure.
- A concave polygon features at least one interior angle greater than 180°.
Regular Polygons
- Regular polygons have all sides and angles congruent.
- Examples of regular polygons include equilateral triangles and squares.
Parallelogram Properties
- In parallelogram ABCD, if m∠ABC = 96°, then m∠ADC equals 96° due to opposite angles being congruent.
- If m∠ABC = 96°, then m∠BAD = 84° since consecutive angles are supplementary.
- Statements not always true for any parallelogram include:
- Diagonals being congruent.
- Diagonals being perpendicular.
- Diagonals of a parallelogram always bisect each other.
Measurement and Relationships
- To find the value of angle z in a parallelogram, one must consider the properties of opposite angles.
- In parallelogram LMNO, if LM = 7x - 4 and NO = 4x + 11, equate and solve for x.
- For the mid-segment of a trapezoid, the measure is the average of the lengths of the two bases.
Specific Quadrilaterals
- A rhombus is defined as a quadrilateral where all four sides are congruent.
- An isosceles trapezoid has legs that are congruent, base angles that are congruent, and diagonals that are congruent.
- A kite is a type of quadrilateral characterized by two distinct pairs of adjacent congruent sides and no parallel sides.
Interior Angles and Sums
- The sum of the interior angles of a polygon with n sides is calculated by the formula (n - 2) × 180°; for a 17-sided polygon, this equals 2700°.
- The measure of an interior angle in a regular decagon (10-sided polygon) is 144°.
Angle Relationships
- In supplementary angles, if m∠1 = 43°, then m∠3 can be found since ∠1 and ∠2 are supplementary and ∠2 and ∠3 are vertical angles; this leads to m∠3 = 137°.
- To find angle measures, utilize known angles, and properties of congruent and supplementary angles.
Properties of Rectangles and Rhombuses
- Not all rectangles have four congruent sides; a rectangle has four right angles and diagonals that bisect each other which is always true.
- For rhombuses, diagonals bisect each other but do not guarantee four right angles.
Studying That Suits You
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Description
Test your knowledge of quadrilaterals with these flashcards from Geometry Chapter 6. Each card presents key concepts, including angles and polygon names, essential for understanding geometric figures. Prepare yourself for your upcoming exam with these helpful review tools.
