Answer:
and 
Step-by-step explanation:
Given
See attachment
Required
Identify the vertical angles
Keynotes
- Vertical angles opposite one another
- Vertical angles are equal to one another
Using the keynote as a reference, we have the following observation from the attachment:
and are opposite
and are congruent
Hence:
and are vertical
<em>(d) is correct</em>
Make a square then cut it in half
<h3>
Answer: Point T is at the location (4, 3)</h3>
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Work Shown:
Let T be the point (x,y)
Point S is defined to be at (2,7)
The x coordinates of S and T are 2 and x in that order. Add them up and divide by 2 to get (2+x)/2. Set this equal to 3 as this is the x coordinate of the midpoint. We have this equation
(2+x)/2 = 3
Now solve for x
(2+x)/2 = 3
2+x = 2*3 .... multiply both sides by 2
2+x = 6
x = 6-2 .... subtract 2 from both sides
x = 4
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We'll follow similar logic and steps for the y coordinate of point T
S = (2,7)
T = (x,y)
The y coordinates for S and T are 7 and y in that order.
Add them up, divide by 2, then set the result equal to 5 (which is the y coordinate of the midpoint). Then solve for y.
(7+y)/2 = 5
7+y = 2*5 ..... multiply both sides by 2
y+7 = 10
y = 10-7 ..... subtract 7 from both sides
y = 3
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Point T gets updated from (x,y) to (4, 3)
ANSWER
EXPLANATION
This means the opposite side is 3 units and the hypotenuse is 4 units.
We use Pythagoras Theorem to find
