Would the hypotenuse of a right triangle with a vertical length of 6 and a horizontal length of 10 have the same slope as the hy
potenuse of the blue and red
triangles shown in the graph?
triangles shown in the graph?
1 answer:
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A diagram of parallelogram MNOP is attached below
We have side MN || side OP and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
<span>∠M ≅ ∠O; ∠N ≅ ∠P
</span>
We have side MN || side OP and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
<span>∠M ≅ ∠O; ∠N ≅ ∠P
</span>
Answer:
see attached
Step-by-step explanation:
Dilation is the transformation that changes the size of something. When you choose ×110% on a copy machine, you are making all the dimensions in the copy equal to 1.1 times the dimensions of the original, for example. That is dilation by a factor of 1.1, or 110%.
Here, you're asked to dilate triangle ABC by a factor of 3. That means all of the dimensions on the dilated figure will be 3 times their length on the original.
The center of dilation is point P. That means all the distances from point P are multiplied by 3.
In the attached figure, a gray arrow has been drawn from point P to each of the points A, B, and C. Then two more arrows of the same length are drawn in the same direction. The total distance at the end of the 3 arrows is 3 times the original distance from point P. These are the points A', B', and C' you are asked to draw. Connecting these points gives the dilated triangle A'B'C'.
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You could think of point P (the center of dilation) as having coordinates (0, 0). Then points A, B, and C would have coordinates A(-4, 0), B(0, -3), and C(-4, -3). To dilate these points by a factor of 3, multiply each coordinate value by 3: A'(-12, 0), B'(0, -9), C'(-12, -9). You will see that these are the coordinates of the vertices of the dilated triangle.
