THIS IS ANOTHER QUESTION I HAVE BEEN STUCK ON FOREVER. I THINK IT REQUIRES TOO MUCH THINKING.
PHILLIP WALKED 100 YARDS TO THE EAST WHILE SHONDRA WALKED 155 YARDS TO THE SOUTHEAST. MEANWHILE, 200 YARDS TO THE NORTH, JOSE WALKED 155 YARDS TO THE WEST AND LUYIN WALKED 100 YARDS TO THE NORTHWEST. THE ANGLE FORMED BETWEEN THE WALKING PATHS OF PHILLIP AND SHONDRA IS CONGRUENT TO THE ANGLE FORMED BETWEEN THE WALKING PATHS OF JOSE AND LUYIN. IF PHILLIP AND SHONDRA ARE NOW 110 YARDS APART, HOW FAR APART ARE JOSE AND LUYIN? HOW DO YOU KNOW?
A. 110 YARDS: SAS CONGRUENCE POSTULATE
B. 310 YARDS: SSS CONGRUENCE POSTULATE
C. 310 YARDS: SAS CONGRUENCE POSTULATE
D. 110 YARDS: SSS CONGRUENCE POSTULATE
I think I would draw this on a a grid.
It helps to draw a picture. The sides of the triangle are congruent, and the angle is also congruent, so by SAS (Side-Angle-Side) Congruence, they are also 110 yards apart.
To find out how far apart Jose and Luyin are, we can use the information given in the question and apply the concepts of congruence.
Let's break down the information step by step:
1. Phillip walked 100 yards to the east.
2. Shondra walked 155 yards to the southeast.
3. Jose walked 200 yards to the north.
4. Luyin walked 100 yards to the northwest.
Now, we need to determine the angle between the walking paths of Phillip and Shondra, and the angle between the walking paths of Jose and Luyin.
The angle formed between the walking paths of Phillip and Shondra is 90 degrees because Phillip walked to the east, and Shondra walked to the southeast (which is intermediate between east and south).
Similarly, the angle formed between the walking paths of Jose and Luyin is also 90 degrees because Jose walked to the north, and Luyin walked to the northwest (which is intermediate between north and west).
Given that the angle between the walking paths of Phillip and Shondra is congruent to the angle between the walking paths of Jose and Luyin, we can conclude that both angles are 90 degrees.
Now, let's determine the distance between Jose and Luyin using the given information:
Jose walked 200 yards to the north, and Luyin walked 100 yards to the northwest. This forms a right triangle, where the distance between Jose and Luyin is the hypotenuse.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
(100^2) + (200^2) = x^2
Simplifying,
10,000 + 40,000 = x^2
50,000 = x^2
Taking the square root of both sides,
x = √50,000 ≈ 223.61 yards
Therefore, the distance between Jose and Luyin is approximately 223.61 yards.
Comparing the options given:
A. 110 yards: SAS Congruence Postulate - This option does not match the calculated distance between Jose and Luyin.
B. 310 yards: SSS Congruence Postulate - This option does not match the calculated distance between Jose and Luyin.
C. 310 yards: SAS Congruence Postulate - This option does not match the calculated distance between Jose and Luyin.
D. 110 yards: SSS Congruence Postulate - This is the wrong option.
So, none of the provided options match the correct answer.
The correct answer is not listed among the options. The distance between Jose and Luyin is approximately 223.61 yards.