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Agenda. Go over homework. Go over Exploration 8.13: more practice A few more details--they are easy. Lots more practice problems. Study hard! And bring a ruler and protractor. Homework 8.2.

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agenda
Agenda
  • Go over homework.
  • Go over Exploration 8.13: more practice
  • A few more details--they are easy.
  • Lots more practice problems.
  • Study hard! And bring a ruler and protractor.
homework 8 2
Homework 8.2
  • 1c. Hexagon, 6 sides, non-convex, no congruent sides, 2 acute angles, 3 obtuse angles, 1 reflex angle, no parallel sides, no right angles…
homework 8 23
Homework 8.2
  • 4. Shape # diagonals
    • Quadrilateral 2
    • Pentagon 5
    • Hexagon 9
    • Octagon 20
    • N-gon
    • each vertex (n) can connect to all but 3 vertices (itself, left, and right). So, n(n-3).
    • But now diagonals have been counted twice. So n(n-3)/2
homework 8 24
Homework 8.2
  • 11. Adjacent, congruent sides. Can be true for:
  • Trapezoid
  • Square
  • Rhombus
  • Non-convex kite
  • Convex kite.
homework 8 25
Homework 8.2
  • 18a
      • Scalene obtuse
homework 8 26
Homework 8.2
  • 18b
      • Equilateral Isosceles
homework 8 27
Homework 8.2
  • 18c.
      • Parallelogram rectangle
homework 8 28
Homework 8.2
  • 18b
      • rectangle rhombus
quadrilaterals
Quadrilaterals
  • Look at Exploration 8.13. Do 2a, 3a - f.
  • Use these categories for 2a:
    • At least 1 right angle
    • 4 right angles
    • 1 pair parallel sides
    • 2 pair parallel sides
    • 1 pair congruent sides
    • 2 pair congruent sides
    • Non-convex
exploration 8 13
Exploration 8.13
  • Let’s do f together:
  • In the innermost region, all shapes have 4 equal sides.
  • In the middle region, all shapes have 2 pairs of equal sides. Note that if a figure has 4 equal sides, then it also has 2 pairs of equal sides. But the converse is not true.
  • In the outermost region, figures have a pair of equal sides. In the universe are the figures with no equal sides.
8 13 2a
8.13 2a
  • At least 1 right angle: A, E, G, J, O, P
  • 4 right angles: J, O, P
  • At least 1 pair // lines: E, F, J - P
  • 2 pair // lines: J - P
  • At least 1 pair congruent sides: not A, B, C, E
  • 2 pair congruent sides: G - P
  • Non-convex: I
slide12
8.13
  • 3a: at least 1 obtuse angle (or no right angle, 1 obtuse and 1 acute angle), 2 pair parallel sides (or 2 pair congruent sides)
  • 3b: at least 1 pair parallel sides,at least 1 pair congruent sides
  • 3c:at least1 pair sides congruent, at least 1 right angle
slide13
8.13
  • 3d: kite, parallelogram
  • 3e:LEFT: exactly 1 pair congruent sides, RIGHT: 2 pair congruent sides, BOTTOM: at least 1 right angle
  • 3f: Outer circle: 1 pair congruent sides, Middle circle: 2 pair congruent sides, Inner circle: 4 congruent sides
try these now

O

P

K, L, M, N

E, G,

Try these now
  • What are the attributes?

parallelogram

1 right angle

try these now15

E

G, J, O, P

D, F

Try these now
  • What are the attributes?

At least 1 right angle

Trapezoid

try this one

J, O, P

E, G

Try this one
  • What are the attributes?

4 right angles

At least 1 right angle

discuss answers to explorations 8 11 and 8 13
Discuss answers to Explorations 8.11 and 8.13
  • 8.11
  • 1a - c
  • 3a: pair 1:same area,not congruent;pair 2: different area, not congruent;
  • Pair 3: congruent--entire figure is rotated 180˚.
warm up
Warm Up
  • Use your geoboard to make:
  • 1. A hexagon with exactly 2 right angles
  • 2. A hexagon with exactly 4 right angles.
  • 3. A hexagon with exactly 5 right angles.
  • Can you make different hexagons for each case?
warm up part 2
Warm-up part 2
  • 1. Can you make a non-convex quadrilateral?
  • 2. Can you make a non-simple closed curve?
  • 3. Can you make a non-convex pentagon with 3 collinear vertices?
warm up part 3

A

F

B

G

C

D

Warm-up Part 3
  • Given the diagram at the right, name at least 6 different polygons using their vertices.

E

a visual representation of why a triangle has 180
A visual representation of why a triangle has 180˚
  • Use a ruler and create any triangle.
  • Use color--mark the angles with a number and color it in.
  • Tear off the 3 angles.
  • If the angles sum up to 180˚, what should I be able to do with the 3 angles?
diagonals and interior angle sum regular
Diagonals, and interior angle sum (regular)
  • Triangle
  • Quadrilateral
  • Pentagon
  • Hexagon
  • Heptagon (Septagon)
  • Octagon
  • Nonagon (Ennagon)
  • Decagon
  • 11-gon
  • Dodecagon
congruence vs similarity
Congruence vs. Similarity

Two figures are congruent if they are exactly the same size and shape.

Think: If I can lay one on top of the other, and it fits perfectly, then they are congruent.

Question: Are these two figures congruent?

Similar: Same shape, butmaybe different size.

let s review
Let’s review
  • Probability:
  • I throw a six-sided die once and then flip a coin twice.
    • Event?
    • Possible outcomes?
    • Total possible events?
    • P(2 heads)
    • P(odd, 2 heads)
    • Can you make a tree diagram? Can you use the Fundamental Counting Principle to find the number of outcomes?
slide25
Probability:
  • I have a die: its faces are 1, 2, 7, 8, 9, 12.
  • P(2, 2)--is this with or without replacement?
  • P(even, even) =
  • P(odd, 7) =
  • Are the events odd and 7 disjoint? Are they complementary?
combinations and permutations
Combinations and Permutations
  • These are special cases of probability!
  • I have a set of like objects, and I want to have a small group of these objects.
  • I have 12 different worksheets on probability. Each student gets one:
    • If I give one worksheet to each of 5 students, how many ways can I do this?
    • If I give one worksheet to each of the 12 students, how many ways can I do this?
more on permutations and combinations
More on permutations and combinations
  • I have 15 french fries left. I like to dip them in ketchup, 3 at a time. How may ways can I do this?
  • I am making hamburgers: I can put 3 condiments: ketchup, mustard, and relish, I can put 4 veggies: lettuce, tomato, onion, pickle, and I can use use 2 types of buns: plain or sesame seed. How many different hamburgers can I make?
  • Why isn’t this an example of a permutation or combination?
when dependence matters
When dependence matters
  • If I have 14 chocolates in my box: 3 have fruit, 8 have caramel, 2 have nuts, one is just solid chocolate!
  • P(nut, nut)
  • P(caramel, chocolate)
  • P(caramel, nut)
  • If I plan to eat one each day, how many different ways can I do this?
geometry
Geometry
  • Sketch a diagram with 4 concurrent lines.
  • Now sketch a line that is parallel to one of these lines.
  • Extend the concurrent lines so that the intersections are obvious.
  • Identify: two supplementary angles, two vertical angles, two adjacent angles.
  • Which of these are congruent?
geometry30
Geometry
  • Sketch 3 parallel lines segments.
  • Sketch a line that intersects all 3 of these line segments.
  • Now, sketch a ray that is perpendicular to one of the parallel line segments, but does not intersect the other two parallel line segments.
  • Identify corresponding angles, supplementary angles, complementary angles, vertical angles, adjacent angles.
name attributes
Name attributes
  • Kite and square
  • Rectangle and trapezoid
  • Equilateral triangle and equilateral quadrilateral
  • Equilateral quadrilateral and equiangular quadrilateral
  • Convex hexagon and non-convex hexagon.
consider these triangles
Consider these triangles

acute scalene, right scalene, obtuse scalene, acute isosceles, right isosceles, obtuse isosceles, equilateral

  • Name all that have:
  • At least one right angle
  • At least two congruent angles
  • No congruent sides
consider these figures
Consider these figures:

Triangles: acute scalene, right scalene, obtuse scalene, acute isosceles, right isosceles, obtuse isosceles, equilateral

Quadrilaterals: kite, trapezoid, parallelogram, rhombus, rectangle, square

Name all that have:

At least 1 right angle

At least 2 congruent sides

At least 1 pair parallel sides

At least 1 obtuse angle and 2 congruent sides

At least 1 right angle and 2 congruent sides