Journal; 1.8.4, geometry

2. Looking at the Consecutive Interior Angles (9 points)

Look at the diagram of the scenario below. A steep downhill ski slope is intersected at an angle by a less steep ski slope. Safety fences need to be set up in the locations shown. The angles of the fences, angles 1 and 2, can be determined by finding the relationship between the angles a and b.


Draw a geometric diagram of this scenario using two parallel lines and one transversal. (Remember that a transversal is a line which cuts across parallel lines.) Label the angles, parallel lines, and transversal as indicated in the diagram above. (2 points)


Starting with the fact that angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, use a two column proof to prove that consecutive interior angles a and b are supplementary. (5 points)
Statement Reason


Explain what the result of your proof tells you about angles a and b. Specifically, if you measured one angle, what would you know about the other? (2 points)


3. The Exterior Angles (6 points)

The fences will be aligned with the exterior angles ∠1 and ∠2. What are some other relationships you can see between ∠1, ∠2, ∠a, and ∠b? (2 points)

Which of the relationships you listed above will be the most helpful in figuring out the measurements of the safety fences? (2 points)

What is the measure of ∠2? (2 points)


4. Reflections (2 points: 1 point each)
Can you think of any other real-life scenarios where parallel lines and transversals exist?



What are the limitations of the ski slope scenario as a real-life example?

The measurement of the angles formed between parallel lines having a common transversal are readily determined by the relationship between the angles

The measures of the angles in the figures are as follows;

2. The required two column proof is presented as follows;

Statement  [tex]{}[/tex]                                                  Reason

∠1 and ∠a are linear pair angles   [tex]{}[/tex]             Given

∠1 + ∠a = 180° [tex]{}[/tex]                                             Linear pair ∠s are supplementary

∠2 and ∠b are linear pair angles   [tex]{}[/tex]            Given

∠2 + ∠b = 180°                                             Linear pair ∠s are supplementary

∠a and ∠b are consecutive interior ∠s   [tex]{}[/tex]   Definition

x║y    [tex]{}[/tex]                                                           Given

∠1 and ∠b are corresponding angles  [tex]{}[/tex]      Definition

∠1 ≅ ∠b   [tex]{}[/tex]                                                     Corr. ∠s formed between║ lines

∠1 = ∠b   [tex]{}[/tex]                                                      Definition of congruency

∠a + ∠b = 180°                                              Substitution property

∠a and ∠b are supplementary  [tex]{}[/tex]                  Definition

The information obtained from the proof is that given ∠1 and ∠b are located in corresponding locations relative to the common transversal of the parallel lines, they (∠1 and ∠b) are equal, and therefore, the the sum of ∠a and ∠b is 180°, given that the sum of ∠1 and ∠a is 180° by substitution property of equality. Which gives that ∠a and ∠b are supplementary angles. Therefore

3. Some of the other relationships between ∠1, ∠2, ∠a, and ∠b, are;

4. A real-life scenario where parallel lines and transversal exist are the handrail and baluster on railings of staircases

The limitations of the Ski slope scenario are;

Learn more about parallel lines having a common transversal here:

https://brainly.com/question/2188951

c. Explain what the result of your proof tells you about angles a and b.

Specifically, if you measured one angle, what would you know about the

other? (2 points)

Simplify by combining like terms.

3x + 4y − 2y + 7x
options:

4x + 6y


10x + 2y


10x + 6y


2y + 4x

NEED HELP This is a picture of a coordinate graph.

Which ordered pair describes a point that is located 4 units to the left of the origin and 6 units below the x-axis?

(4, −6)
(6, −4)
(−4, −6)
(−6, −4

what is the surface area of this design?

PLZ HELP ME :( you can pick both neither of one of the triangles

What if the driver of the Ferrari 550 was cruising along and suddenly hit the brakes to stop because she saw a cat on the road? She skidded to a stop, and fortunately, missed the cat. When she got out of the car she measured the skid marks left by the car so that she knew that her braking distance was 31 ft. How fast was she going when she hit the brakes?

Mario spent $5.86 for a drink and a sandwich. His drink cost $1.34. How much did Mario spend on the sandwich. Create and solve an equation that represents this situation.

I think i got an answer but i want to make sure its correct

The diagram shows triangle ABC.
Which statement would prove that triangle ABC is a right triangle?
a. The slope of segment AB and the slope of segment BC = 1
b. The slope of segment AB and the slope of segment BC = -1
c. The slope of segment AB is 1 and the slope of segment BC is -1
d. The distance from A to B is equal to the distance from B to C

Someone answered this question with a link that didn't work so i need help

Find the area of the rectangle:

A four-sided sandbox has more than two right angles, two side lengths 3 ft, and two side lengths 6 ft.
What geometric shape best describes the shape of the sandbox? Use pencil and paper. Sketch the
sandbox.
Which geometric shape best describes the shape of the sandbox?

A chef cooked vegetables for 22 customers. The chef cooked 1/3 pound of potatoes and
1/4 pound of green beans for
each customer.

How many pounds of vegetables did the chef cook for these customers all together?

Using the distributive property, what number goes on the line to make the equation true?

__ (3+2)= 36+24

12. Divide 2.4 ; 2= 14 1 1​

PLEASE HELP! 15 POINTS!

ABC and is a straight line

Work out the length of AC
Give your answer to 1 decimal place

PLEASE HELP
I have no idea how to do this

$6.00+$8.00 =
answer

Solve for x
−3x ≤−18
​

What is the distance from the origin to point A graphed on the complex plane below?

Find the area please!

1/3 (x-10) = -4
what is x?

juan drove 126 miles in 3 hours. If he continued at the same rate, how long would it take to travel 336 miles? ​

40) If you deposit $6000 in a bank account
with an interest rate of 5% compounded
monthly, find the balance after 6 years.
A) 4442.12 B) $8084.11
C) $8094.11 D) $7618.41
E) $4436.51

How do you do this equation?
2(m+7)= blank m+ blank
Use properties of operations to complete the equivalent expression.

Add.

58+28













































Item 19
Which number is prime?

4

9

21

23


1016

78

716

18

Can you please help me

Kade has 100 flag pins. He has 221 frog pins and 10 dinosaur pins. How many flag and frog pins does Kade have?

6. A leather bag is bought for Rs 18000 and sold with 15% loss. Find the selling price of the bag.​

plz help

Which of the following uses the reciprocal property to rewrite x/5 = 72/4?

A. 5/x = 4/72

B. x/4 = 5/72

C. x/5 = 72/4

Write an equation and slope intercept form of the line that passes through the given points

AB is the diameter of the circle shown. The radius is 8.5 cm, and AC = 8 cm. Find the following values using the visual given below.