Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockw
ise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are: 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s? w x y z
2 answers:
Answer: Angle w and angle z should equal 92° to prove that r║s
Step-by-step explanation: Let us start by constructing the lines r and s, and then draw a transversal to intersect both lines as stated in the question. At the intersection of lines m and r, we have clockwise from the top angles w, x and the other two blank. This is as shown in the picture attached.
Also at the intersection of lines m and s, clockwise from the top, the angles are 92, y, z and a blank. This is also clearly marked in the picture attached.
If the two lines r and s are parallel, then it means;
(1) Angle 92 is equal to angle z (opposite angles are equal)
(2) Angle z is equal to the blank underneath angle x (corresponding angles on two parallel lines are equal)
(3) Angle 92 is equal to the blank underneath angle x (alternate angles on two parallel lines are equal)
(4) Angle 92 is equal to angle w (corresponding angles on two parallel lines are equal)
Therefore, of all four angles marked as w, x, y and z angles w and z should equal 92° to prove that line r is parallel to line s.
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Answer:
15 feet
Step-by-step explanation:
It is given that Quadrilateral ABCD is similar to Quadrilateral EFGH. This means that the corresponding sides of these two quadrilateral will be in the same proportion.
i.e.
Ratio of two corresponding sides would be the same. We are given longest three sides of ABCD and shortest two sides of EFGH. Let the 4th sides of ABCD i.e. the shortest side be x.
So, the ratio of the shortest sides of two quadrilaterals would be the same as the ratio of second shortest sides.
So,
So, the 4th side on quadrilateral ABCD would be 15 feet. None of the options match with the answer.
Answer:
a) The coordinates of the missing vertex = (7, 8)
b) Area = 18 square units
Perimeter = 18 units
Step-by-step explanation:
a) We know three of the four vertices:
A: (4, 2) C ______ D(?)
B: (7, 2) | |
C: (4, 8) A |______| B
To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:
Hence, the distance of point D from point C in the x-direction is:
Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:
Then, the distance of point D from point B in the y-direction is:
Therefore, the coordinates of the missing vertex (point D) are:
b) The area of the rectangle is:
The perimeter is given by:
I hope it helps you!