The two triangles are similar by the AA Similarity theorem.
The height of the tree can be calculated by figuring out the ratio between the distance between the mirror to her feet and the distance from the mirror to the tree
<h3>How to use the concept of similar Triangles?</h3>
From Law of Reflection, we know that the angle of incidence and the angle of reflection are equal to each other.
Now, triangles can be proved similar by the AA, SAS, or SSS theorems. However, in this question, the triangles as seen in the attached image can be proved similar by the AA similarity theorem.
This is because both triangles have one congruent angle in common.
Sarah and the tree are standing straight and perpendicular to the ground and as such, the angles formed by Sarah and the tree are right angles.
The above tells us that the two triangles have two angles in common, making them similar triangles by the AA (Angle Angle) similarity theorem.
Since the triangles are similar, it means that the ratios of the sides of the triangles will be the same. Thus, if Sarah knows the distance from the mirror to her feet and the distance from the mirror to the tree, she can create the ratio between the two triangles.
Read more about Similar Triangles at; brainly.com/question/14285697
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The point will be at (-1, 3). Use the x value that has only been used once, -1, and the y value that has only been used once. (6,0) and (6, 3) are on the same side vertically of the rectangle because their x values are the same. Because 6 > -1, you know that they make up the right side of the rectangle. (-1,0) and (6, 0) both have the same y values, so they are on the same side horizontally, and are the bottom of the rectangle because 0<3. This all means the fourth point is the rectangles's top left corner. Because it is a rectangle, its sides are parallel, so you know that it will have the same x value as the left bottom point (-1,0) and the same y value as the right top point, (6, 3).
Hello,
For the first question, congruent triangles have congruent corresponding angles and sides. For option choice A, MN corresponds with PQ, not PR, so it is incorrect to conclude that they are equal. The answer is A.
For the second question, we are given two angles and an not included side, so it would be AAS.
The answer is A, I believe.
Hope this helps!
Answer:
She spent 4/6 of her free time.
Step-by-step explanation:
1/6 + 3/6 = 4/6
Answer:
So on this case the 98% confidence interval would be given by (3.767;4.233)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=100 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.98 or 98%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 98% confidence interval would be given by (3.767;4.233)