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A Geometry > Unit 8 - Quadrilaterals > Flashcards

Unit 8 - Quadrilaterals Flashcards

1
Q

What is a trapezoid? (3)

A
  1. A quad that has AT LEAST one pair of parallel sides
  2. Parallel Sides = Bases
  3. Nonparallel Sides = Legs
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2
Q

What are the three main points that proves an isosceles trapezoid?

A
  1. Must have at least one pair of congruent opposite sides
  2. Each pair of base angles are congruent
  3. Diagonals are congruent
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3
Q

Why do you only have to prove only one set of base angles to be congruent in a proof?

A

Other angles are congruent thru consecutive interior angles

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4
Q

What is the trapezoid midsegment/median theorem? (4)

A
  1. Midsegment and Median are the same
  2. Midsegment is parallel to the base
  3. It’s measure is 1/2 of the sum of the bases
  4. Essentially, it is taking the average of the bases
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5
Q

What are the 4 properties of a parallelogram?

NOTE: PARALLELOGRAM IS A TRAPEZOID, NOT AN ISOCELES TRAPEZOID

A
  1. Opp. Sides are parallel
  2. Opp. Sides are congruent
  3. Opp. angles are congruent
  4. Diagonals bisect each other
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6
Q

Why does a rt. angle in a parallelogram mean the other 3 angles are also right? (2)

A
  1. Opp. Angles are congruent, making the other angle rt.
  2. Consecutive Interior forces the other angles to be rt.
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7
Q

What is the rule when it comes to the diagonals of a parallelogram? (2)

A
  1. Diagonals of a Parallelogram Bisect Each Other
  2. Diagonals form two congruent triangles (YOU WILL STILL HAVE TO PROVE)
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8
Q

What are the five ways to prove a parallelogram?

A
  1. Both pairs of opp. sides are congruent
  2. Both pairs of opp. sides are parallel
  3. Both pairs of opp. angles are congruent
  4. Diagonals bisect each other
  5. ONE pair of opp. sides are parallel & congruent
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9
Q

What is something to keep in mind with when proving properties of a quadrilateral?

A

You may use all the properties that the quadrilateral posess except for the properties you are trying to prove.

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10
Q

When you are stating that something is a parallelogram, rectangle etc., what do you put in the reason box?

A

A quadrilateral with (property) is a (parallelogram, rectangle, isoc. trapezoid, etc.)

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11
Q

What should you do when proving a rectangle? (2)

A

Prove that is a parallelogram first, then use the following two properties to prove that the parallelogram is a rectangle:

  1. One right angle (rect. has 4 rt. angles)
  2. Diagonals are congruent (rect. is also an isoc. trapezoid)
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12
Q

What are the properties of a rectangle? (5)

A
  1. Diagonals are congruent
  2. Diagonals bisect each other (can form isosceles triangles)
  3. Opposite sides are congruent
  4. Opposite sides are parallel
  5. Has 4 right angles (all angles are congruent)
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13
Q

What are the properties of a rhombus? (5)

A
  1. Opposite Sides are Parallel
  2. ALL sides are congruent
  3. Diagonals are angle bisectors
  4. Diagonals bisect each other
  5. Diagonals are perpendicular
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14
Q

What are the properties of a square? (7)

A
  1. ALL sides are parallel
  2. ALL sides are congruent
  3. ALL angles are right
  4. Diagonals are angle bisectors
  5. Diagonals bisect each other
  6. Diagonals are congruent
  7. Diagonals are perpendicular
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15
Q

How do you prove a rhombus? (4)

A
  1. Must prove it is a parallelogram first
  2. Diagonals are perpendicular
  3. Pair of consecutive sides are congruent
  4. A diagonal bisects one set of angles
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16
Q

How do you prove a square? (4)

A
  1. Prove it is a parallelogram
  2. Prove it is a rectangle
  3. Prove it is a rhombus
  4. A parallelogram has one property of a rhombus & rectangle, it’s a square
17
Q

What are the properties of a kite? (4)

A
  1. 2 pairs of consecutive sides are congruent
  2. Diagonals are perpendicular
  3. At least 1 pair of opp. angles congruent (between non congruent sides)
  4. Diagonals bisect angles
18
Q

Why are the angles in a kite congruent and angle bisectors exist?

A

The kite is split into two congruent triangles through SSS, and the angles and bisectors are CPCTC.

19
Q

How to prove a quad. to be rhombus/kite thru perpendicular diagonals

A

(When they give you the rt. angle)
Statement - Diagonals (Segments name) are perpendicular
Reasoning - Perpendicular Lines form Right Angles

Statement - A quad is a rhombus
Reasoning - In kite/rhombus, diagonals are perpendicular to each other

A Geometry (20 decks)

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