bill533:
https://i.imgur.com/68KuvZW.jpg
bill533:
@SmokeyBrown
SmokeyBrown:
One way you can do this type of problem is to find which points match each other. Here, point M on the right shape matches point S on the left shape; point L matches point R; N matches T; and K matches Q. Now, you may notice that the left shape and the right shape are horizontal reflections of each other. So, that narrows our choices down choice A and choice D. Which set of instructions can we use to re-position the left shape so that it overlaps the right shape?
bill533:
D
SmokeyBrown:
Yup, I agree. If we perform the transformations in choice D, you'll see that the shapes are congruent
bill533:
ok the answer is D correct with the explanation
bill533:
RIGHT ?
SmokeyBrown:
Yup, that's right
SmokeyBrown:
Well, we know that AB is perpendicular to CD, so the angle on both sides is 90 degrees. And CD is bisecting AB, which means AB is being split into two equal halves on each side. Now, if we draw triangles like the question mentioned, they'll be sharing a side, XM. So, the triangles have 2 sides and an angle confirmed to be in common. Which would be the appropriate rule to use in this situation?
bill533:
C
SmokeyBrown:
Yup, very nice
SmokeyBrown:
So, the shape shown in the picture has vertices in quadrants I II and IV, but once reflected over the y-axis it'll be in quadrants I II and III. So I'd go with C for that one. I'll have to go with D for the second one, since that's the only set of instructions that puts the entire shape into quadrant IV, in the bottom right.
SmokeyBrown:
I'm pretty sure B is the answer here, since the definition of a median is pretty much in the answer.
SmokeyBrown:
C would be the best answer here, since those conditions do guarantee that point C falls on the line described.
SmokeyBrown:
For the first one, a+c=c+b because the angle measure of a straight line is always 180. The symmetric property is the right choice, since a and b are already given as equal For the second one, c=c is true because of the reflexive property And for the third one, a=b is true because of the transitive property, by combining what we learned from the previous steps
SmokeyBrown:
Oh, well I guess the last one would be the "subtractive rule" since you subtract c from both sides to get that result
SmokeyBrown:
I think only a would be congruent to b and c would be congruent to d
SmokeyBrown:
I think the next step would be to show that angle 3 is congruent to angle 5. From there, you'd show that angles 1+2+3 = 180, so angles 4+2+5 must also equal 180
bill533:
the first one is A right ?
SmokeyBrown:
I'd say b for this one. And yeah, the first one would be a
SmokeyBrown:
Oh, reflecting one of the triangles over the altitude line would make it overlap the other triangle, proving that they are congruent. So, a would be your answer
SmokeyBrown:
First one is the definition of complimentary angles, two angles that add together to total 90 degrees. Second one would be m2 + m3 Third one would be subtraction property of equality And the last one would be the definition of congruent angles
SmokeyBrown:
Well, b describes the proof we just did, so I'd go with that
SmokeyBrown:
For the first one, I think there are 8 possible rotations between 1 and 360 degrees, including 360 degrees, that carry the octagon onto itself. For the second one, a, b and c are true, but d and e are not. You can try for yourself to see the result of the transformations
SmokeyBrown:
First one is "angle 2 is congruent to angle 3", because they are vertical angles The second one is "corresponding angles are congruent" The third one is "two angles are congruent to the same angle, so they are congruent"
SmokeyBrown:
I think angles 4 and 5 are alternate interior angles, so c would be the best choice
SmokeyBrown:
Oh yeah, that's the definition of a circle.
SmokeyBrown:
I think that c d and e are all correct here
SmokeyBrown:
I think it'd be the side side angle rule, then the definition of congruent angles for the second one
bill533:
https://i.imgur.com/qlRbLHf.jpg https://i.imgur.com/8OABAhx.jpg https://i.imgur.com/PRCEubJ.jpg https://i.imgur.com/zVKXk7F.jpg
SmokeyBrown:
90 degrees; translation; up 4 units
SmokeyBrown:
Originally, point H is 3 units to the left and 4 units up from point G. After being rotated 90 degrees clockwise, point H would be 3 units up and 4 units to the right of G. The answer would be b (3,6). That's also the only answer in quadrant 1, which you can tell the point must be in.
SmokeyBrown:
1 and 5 are corresponding angles, which are congruent. 5 and 7 are vertical angles, which are congruent. 1 is congruent to 5, 5 is congruent to 7, so 1 and 7 are congruent.
SmokeyBrown:
So, I'm thinking the points of the new garden will be (-12,0) (0,8) and (0,0)
SmokeyBrown:
The angle measures of the new garden would be the same as the original. I'm sure you're able to calculate that for yourself
bill533:
i'm not sure
SmokeyBrown:
Well, remember that a triangle's angles add up to 180 degrees. And a right angle is 90 degrees. Then, one of the angles is labeled with its measurements. From there, you can find the measure of the third angle.
bill533:
you selected c d and e
SmokeyBrown:
Well, in that case just c and d. I must have been wrong about e
bill533:
Lucy, Ricky, and Ethel are competing in a cooking competition. They all used different amounts of flour from a can containing 6 pounds of flour. Lucy used 15% of the total flour in the can Ricky used 0.13 of the total flour in the can Ethel used4/5 pound of the total flour in the can Who used the greatest amount of flour from the can? Explain your reasoning and show your work proving your reasoning is correct.
SmokeyBrown:
Well, 15% of the flour in the can is 0.9 pounds. Then, 0.13 is definitely lower than 15%, since 15% is equal to 0.15 of the total 4/5 pounds is 0.8 pounds. So, the largest amount of all these is 15% with 0.9 pounds
bill533:
ok back to the measure of the third angle is 59 right ?
SmokeyBrown:
Not quite, no. 90 + 59 + 56.3 would be 196.3, which is a little higher than 180
bill533:
oh it's 196.3
SmokeyBrown:
No, that can't be the measure of the missing angle. 90 + 56.3 + [missing angle] would equal 180, but 196.3 is already greater than 180.
SmokeyBrown:
So, the missing angle would have to be less than 50
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