Vocab
Define the following and include the symbol that represents the vocab, if any:
complementary angles
vertex
adjacent
perpendicular
complementary: angles that add up to 90 degrees
vertex: the point connecting the 2 rays of an angle
adjacent: touching or sharing sides
perpendicular: lines that form a 90 degree (right) angle ; symbol = ⊥
Take a look at the example of parallel lines and traversals (Fig. 4). Identify 4 each:
alternate exterior angles
corresponding angles
Check with tutor.
From a train station, one train heads north and another heads east. Some time later, the northbound train has traveled 16 miles. If the two trains separated by a straight-line distance of 20 miles, how far has the eastbound train traveled?
The train will have traveled just over 12 miles, 12.12 mi to be precise.
Show me you remember all trig ratios:
sine = ?
cosine = ?
tangent = ?
What do we use inverse trig functions for, like sin-1? Note, sometimes these are called arc functions (like arcsin).
sine = opp/hyp
cosine = adj/hyp
tangent = opp/adj
Inverse trig functions undo the the function, which allows us to solve variables with trig functions applied to them.
What is Mr. O's favorite color?
Bonus: 50 points if you know his second favorite color.
Green! Second favorite: orange.
Describe the following in your own words; include the symbol that represents the vocab, if any:
supplementary angles
a plane
collinear
coplanar
supplementary angles: add up to 180 degrees
plane: a flat surface that stretches out (generally, infinitely, but we talk about bounded planes all the time)
collinear: points (or things) on the same line
coplanar: points (or things) on the same plane
Use what you know about supplementary angles to find X.
(Fig. 1)
x = 21
Answer both a) and b) for Fig. 7. Ivan is standing on point A, where streamers will be fastened for a party.
Round answers to the hundredth.
He's 4.47 m from corner R;
he's 10.77 m from corner S.
No figure this time! A ramp is pulled out of the back of truck. There is a 38 degrees angle between the ramp and the pavement. If the distance from the end of the ramp to to the back of the truck is 10 feet. How long is the ramp?
x = 12.69 ft
How many dogs did Mr. O have growing up?
Total of 5: Honey, Bandit, Tucker, Tipper, Gunder
We also fostered a couple dogs: Harley, Daisy, Luke
Show me you haven't forgotten triangles and define:
scalene
obtuse
isosceles
acute
scalene (triangle) = no same length sides
obtuse (angle) = more than 90 degrees
isosceles (triangle) = 2 sides equal length
acute (angle) = less than 90 degrees
Two lines meet at a point that is also the vertex of an angle. Set up and solve an equation to find the value of 𝑥. Explain why your answer is reasonable.
(Fig. 6)
x = 128
Explanations will vary; check with tutor.
Consider Fig. 9. What are 2 different ways you could attack the problem to get the answer? Explain your answer.
x = 5
Could use complementary (7x + 9 + 136 = 180) or supplementary (136 + x = 180 ; x = 44, so 7x + 9 = 44) theorems to solve.
Consider Fig. 14. A zip-line runs from a tree to a landing across a deep valley. What is the width, w, of the valley?
w = 72.75
(rounded to the hundredths)
Name 5 of Mr. O's hobbies.
Check with Mr. O - some examples:
Writing, snowboarding, reading, chess, anime, video games, piano, etc.
What is the law of sines?
sin A/a = sin B / b = sin c / c
Identify opposite interior angles, then solve for X.
(Fig. 3)
Check with tutor.
x = 29
Use Fig. 10 to make an argument about the following:
During a game of pool, your friend claims they can make the shot shown in the Fig. 10 by hitting the cue ball so that m∠1 = 25°. Is your friend correct? Explain.
Various answer. Check with tutor.
A surveyor makes the measurements shown to determine the length of a bridge to be built across a small lake from the North Picnic Area to the South Picnic Area (Fig. 13). Find the length of the bridge.
The length of the bridge will be about 172.1 meters.
Name at least 3 martial arts Mr. O knows.
Bonus: extra 50 points if you can guess how many he knows total in 1 try.
Budo Taijitsu (Ninjutsu), karate (hand-to-hand), Judo (grappling/throwing), Kendo (fencing), Iado (slashing from the draw), and Arnis (hand-to-hand, small weapons).
That's right, kids, that's a total of 6!
What is the law of cosines?
c2 = a2 + b2 − 2ab cos(C)
(or a similar permutation)
Check the angle bisector on the board. Using what you know about bisectors, find x. Explain your answer.
(Fig. 5)
x = 12
Consider Fig. 11, a prototype for a case you're designing. Use the information in the figure to answer a), b), and c).
a) m<2 = 70
m<3 = 110
b) <ABC forms a line because its degree measure = 180.
c) More steep, the small the angle, the sharper/steeper the hypotenuse. We can show by drawing a bisecting line in <1; if the line is steeper, a smaller degree measure (60<70) makes a steeper opening.
An creature's step angle is a measure of walking efficiency. The closer the step angle is to 180°, the more efficiently it is to walk. The diagram (Fig. 12) shows a set of footprints for a dinosaur.
Find the step angle B.
B = 127.3 degrees
Does Mr. O have siblings? If so, how many? Is he and only child, the oldest, or the youngest?
Bonus: extra 50 to anyone who can remember his/her/their name(s).
He has an older brother, Matt, and a younger sister, Jamie.
That means he's not the oldest or youngest, but the middle child.