• 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.

• 1c. Hexagon, 6 sides, non-convex, no congruent sides, 2 acute angles, 3 obtuse angles, 1 reflex angle, no parallel sides, no right angles…

• 4. Shape # diagonals
– Quadrilateral
– Pentagon
– Hexagon
– Octagon
2
5
9
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

• 11. Adjacent, congruent sides. Can be true for:
• Trapezoid
• Square
• Rhombus
• Non-convex kite
• Convex kite.

• 18a
• Scalene obtuse

• 18b
• Equilateral Isosceles

• 18c.
• Parallelogram rectangle

• 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

• 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.

• 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

• 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 least 1 pair sides congruent, at least 1 right angle

• 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

• What are the attributes?
parallelogram
1 right angle
E, G,
O
P
K, L,
M, N

• What are the attributes?
Trapezoid At least 1 right angle
E
D, F
G, J,
O, P

• What are the attributes?
4 right angles
At least 1 right angle
J, O, P
E, G

• 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˚.

• 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?

• 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?

• Given the diagram at the right, name at least 6 different polygons using their vertices.
A
B
G
C
F
D
E

• 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?

• Triangle
• Quadrilateral
• Pentagon
•
•
• Hexagon
• Heptagon (Septagon)
• Octagon
• Nonagon (Ennagon)
• Decagon
11-gon
Dodecagon

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, but maybe different size.

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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.

• Kite and square
• Rectangle and trapezoid
• Equilateral triangle and equilateral quadrilateral
• Equilateral quadrilateral and equiangular quadrilateral
• Convex hexagon and non-convex hexagon.

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

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