Answer:
ΔDAM ≅ ΔTUM according to Side Angle Side (SAS) rule of congruency
Step-by-step explanation:
The proof of congruency of the two triangles is as follows;
Statement Reason
Segment DM is congruent to Segment TM Given
Segment AM is congruent to Segment UM Given
∠DMA is congruent to ∠UMT Given
Therefore, ΔDAM is congruent to ΔTUM SAS rule of congruency
Where;
SAS = Side Angle Side
Therefore;
ΔDAM ≅ ΔTUM according to Side Angle Side (SAS) rule of congruency.
Answer:
A) 4
Step-by-step explanation:
There are a couple of ways to get this but this is how I did it:
1. Multiply the second equation by 1/4 to get the same fraction for y as the one in the first equation
1/4 x + 1/8 y = 2
1/4 (1/3 x + 1/2 y = 4)
1/12 x + 1/8 y = 1
2. Subtract the first equation from the new equation
1/12 x + 1/8 y = 1
<u> - 1/4 x - 1/8 y = -2</u>
-1/6 x= -1
3. Divide both sides by -1/6
<u>-1/6</u> x= <u>-1</u>
-1/6 -1/6
x = 6
4. Substitute 4 in for x in the original equation:
1/4 (6) + 1/8y = 2
6/4 + 1/8y = 2
1/8y = 1/2
y = 4
<h3>
Answer: Slope = -2/3</h3>
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Explanation:
Let's compute the slope of the line through the two original points
m = (y2-y1)/(x2-x1)
m = (4-10)/(7-(-2))
m = (4-10)/(7+2)
m = -6/9
m = (-2*3)/(3*3)
m = -2/3
The slope is -2/3
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Now apply the scale factor.
We'll multiply each coordinate of each point by 2
(-2,10) becomes (-4,20) after multiplying each coordinate by 2
(7,4) becomes (14,8) after multiplying each coordinate by 2
Let's find the slope of the line through (-4,20) and (14,8)
m = (y2-y1)/(x2-x1)
m = (8-20)/(14-(-4))
m = (8-20)/(14+4)
m = -12/18
m = (-2*6)/(3*6)
m = -2/3
We get the same slope. This isn't a coincidence. Dilating a set of points will preserve the slope of the line through those points.
If A and B are the two original points, and A' and B' are the dilated counterparts, then the slope of line AB is the same as the slope of line A'B'.
The scale factor doesn't affect the answer.
Answer:
x=-4
Step-by-step explanation:
Since the line is vertical it must be in the form
x = x coordinate
Here it is -4 so it is
x=-4
Answer:
87
Step-by-step explanation:
Complementary angles add to 90 degrees
Let c be the complement
c + 3 = 90
Subtract 3 from each side
c+3-3 = 90-3
c = 87