Daily Scribe

Today in class we wrapped up on a few different subjects, including ratios. There is to be a quiz on Thursday.

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We also began Labsheet 4.3, on page 64.

Here are the answers to the problems.

A) The value of X is 10 centimeters. This is because the scale factor happens to be (from the smaller shape to the larger shape) multiply by 2. Since X's similar side on the smaller shape is 5 centimeters, and 5 * 2 = 10 centimeters.

This is one example of using a scale factor to solve a problem.

B) The value of X is 13.75, because the scale factor of the smaller shape to the larger shape is multiply by 2.5. Using the same method as before, we learn that the side similar to X is 5.5 centimeters. 5.5 * 2.5 = 13.75.

C) The value of X is 2.5, because the scale factor from the larger shape to the smaller shape is divide by4. X's similar side on the larger shape is 10 centimeters in length, so 10 divided by 4 = 2.5.

D) Finding the measurement of angle B is easy. It is 68 degrees. This is because B and the other angle measuring 68 degrees are congruent. This means that they both have the same measurements.

Finding angles A and C is more challenging. They must be found using a number of clues.

First of all, since they are congruent, you know that they will have the same measurements.

Next, since an average parallelogram has angles adding up to 360 degrees, you must take the sum of the two angles whose measurements have already been determined (68 and 68, which adds up to 136) and subtract that sum from 360. 360-136 = 224.

Finally, since you now know that the sum of the two angles is 224, and that both angles must have the same measurements (because they are congruent) it only makes sense to divide 224 by 2.

224 divided by 2 = 112. Therefore, angles A and C are both 112 degrees.

In order to check that this is correct, all you have to do is add every angle together and see if the sum is 360. 68+68+112+112= 360 degrees. This proves that the angles have been measured correctly.


E) 1: The value of X can be found by using the scale factor. The scale factor from the larger shape to the smaller shape is divide by 1.75. So, since X's similar side on the larger shape is 1.75, the value of X is 1.
2: Again, the value can be found by using scale factors. Since Y's similar side on the smaller shape is 4, and 4 * 1.75.= 7, the value of Y is 7.
3: The area of the larger shape is 147. This is because the height adds up to 10.5, and the length is 14. 10.5 * 14 = 147.
4: The area of the smaller shape can be found by using the same strategy used during problem 3. The base of the smaller shape is 8, and the height is 6. 8 * 6 = 48, so the area of the smaller shape is 48.

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Those are the answers to Labsheet 4.3, done in class today.

As previously mentioned, there will be a quiz on Thursday, so study hard!



Written by Grace T