Agenda

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# Agenda - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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 8.2
• 4. Shape # diagonals
• 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 8.2
• 11. Adjacent, congruent sides. Can be true for:
• Trapezoid
• Square
• Rhombus
• Non-convex kite
• Convex kite.
Homework 8.2
• 18a
• Scalene obtuse
Homework 8.2
• 18b
• Equilateral Isosceles
Homework 8.2
• 18c.
• Parallelogram rectangle
Homework 8.2
• 18b
• rectangle rhombus
• 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
• 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
• 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
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
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

O

P

K, L, M, N

E, G,

Try these now
• What are the attributes?

parallelogram

1 right angle

E

G, J, O, P

D, F

Try these now
• What are the attributes?

At least 1 right angle

Trapezoid

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
• 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
• 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
• 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?

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˚
• 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)
• Triangle
• Pentagon
• Hexagon
• Heptagon (Septagon)
• Octagon
• Nonagon (Ennagon)
• Decagon
• 11-gon
• Dodecagon
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
• Probability:
• I throw a six-sided die once and then flip a coin twice.
• Event?
• Possible outcomes?
• Total possible events?
• Can you make a tree diagram? Can you use the Fundamental Counting Principle to find the number of outcomes?
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
• 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
• 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
• 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
• 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?
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
• Kite and square
• Rectangle and trapezoid
• Equilateral triangle and equilateral quadrilateral
• Convex hexagon and non-convex hexagon.
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:

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