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Questions and Answers
What is a quadrilateral?
In a trapezoid, what are the non-parallel sides called?
What defines a kite as a quadrilateral?
Which parallelogram has four right angles?
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What property is guaranteed for any two opposite sides of a parallelogram?
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What is the primary condition that guarantees a quadrilateral is a parallelogram?
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If a quadrilateral has both pairs of opposite sides congruent, what shape is it most likely to be?
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What is the shape of a quadrilateral if one pair of opposite sides is both congruent and parallel?
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What is a property of a rectangle related to its diagonals?
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If a trapezoid has congruent base angles, what type of trapezoid is it most likely to be?
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What theorem states that a line parallel to one side of a triangle intersects the other two sides proportionally?
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What conditions make two triangles similar?
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Study Notes
Quadrilaterals
- A quadrilateral is a four-sided polygon.
- Parts of a polygon include sides, vertices, angles, and diagonals.
Types of Quadrilaterals
- Parallelogram: a quadrilateral with two pairs of parallel sides.
- Trapezoid: a quadrilateral with one pair of parallel sides.
- Parts of a trapezoid include parallel sides (bases), non-parallel sides (legs), and base angles.
- Isosceles trapezoid: a trapezoid with congruent legs.
- Kite: a quadrilateral with two distinct pairs of congruent and adjacent sides.
- Rectangle: a parallelogram with four right angles.
- Rhombus: a parallelogram with four congruent sides.
Properties of Parallelograms
- A diagonal forms two congruent triangles.
- Any two opposite angles are congruent.
- Any two consecutive angles are supplementary.
- Any two opposite sides are congruent.
- The diagonals bisect each other.
Triangle Congruence
- Ways to prove a theorem include:
- A statement of the theorem
- A drawing under consideration
- A statement of what is given
- A statement of what is to be proved
- An orderly arrangement of statements and reasons
- Triangle congruence theorems include SSS, SAS, ASA, and AAS.
Properties of Special Parallelograms
- Conditions guaranteeing that a quadrilateral is a parallelogram include:
- Congruent opposite sides
- One pair of congruent and parallel opposite sides
- Congruent opposite angles
- Bisecting diagonals
- Properties of rectangles include:
- Congruent diagonals
- At least one right angle
- Properties of rhombuses include:
- Perpendicular diagonals
- Bisecting diagonals
- Each diagonal bisects the opposite angles
- Properties of squares include:
- Bisecting diagonals that bisect the vertex angle
Properties of Trapezoids
- Properties of isosceles trapezoids include:
- Congruent base angles
- Congruent diagonals
- The median of a trapezoid is parallel to its bases and is half of the sum of the lengths of the bases.
Ratio and Proportion
- A ratio is a comparison between two positive quantities, expressed as a:b or a/b.
- A proportion is a statement of equality between two ratios.
- The first and fourth terms of a proportion are called the extremes, while the second and third terms are called the means.
Triangle Proportionality
- The Basic Proportionality Theorem states that if a line parallel to one side of a triangle intersects the other two sides in distinct points, then it divides the sides proportionally.
Similar Figures
- Correspondence refers to the relationship between similar parts of two polygons.
- Similar polygons have congruent corresponding angles and proportional corresponding sides.
- Similar triangles have congruent corresponding angles and proportional corresponding sides.
- Similarity theorems include the AAA Similarity Theorem.
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Description
Learn about quadrilaterals in this lesson, covering the definition, parts including sides, vertices, angles, and diagonals. Also explore different kinds of quadrilaterals like parallelograms and trapezoids.
