Answered

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Lesson 6 Practice Problems

1. A rectangle has side lengths of 6 units and 3 units. Could you make a quadrilateral that is not identical using the same four side lengths? If so, describe it.

2. Provide an example of three side lengths that cannot possibly form a triangle, and explain how you know.

3. Find [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex].

How many right angles need to be put together to make:
a. 360 degrees?
b. 180 degrees?
c. 270 degrees?
d. A straight angle?

Sagot :

GinnyAnswer
Certainly! Let's tackle each question step-by-step:

### Question 1
Could you make a quadrilateral that is not identical using the same four side lengths (6 units and 3 units)?
Yes, you can make a quadrilateral that is not a rectangle with four sides consisting of the lengths 6 units and 3 units.

Explanation:
If you take the sides of 6 units and 3 units and arrange them as follows:
- Two sides of 6 units
- Two sides of 3 units

You could create a quadrilateral like a parallelogram that is not necessarily a rectangle. For example, if the opposite sides are equal (6 units opposite to 6 units and 3 units opposite to 3 units) and the angles between them are not 90 degrees, it forms a parallelogram, which is not identical to the given rectangle.

### Question 2
An example of three side lengths that cannot make a triangle, and how you know:
Let's consider the side lengths 1, 2, and 4.

Explanation:
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For the side lengths 1, 2, and 4:
- 1 + 2 = 3, which is not greater than 4.

Therefore, these sides do not satisfy the triangle inequality theorem, and hence, they cannot form a triangle.

### Question 3
Number of right angles required to form various angle measures:

a. 360 degrees
To make a full circle, 360 degrees is necessary. Since each right angle is 90 degrees:
- Number of right angles needed: [tex]\( \frac{360}{90} = 4 \)[/tex]

b. 180 degrees
For a straight angle, 180 degrees is needed. Since each right angle is 90 degrees:
- Number of right angles needed: [tex]\( \frac{180}{90} = 2 \)[/tex]

c. 270 degrees
For 270 degrees, we consider:
- Number of right angles needed: [tex]\( \frac{270}{90} = 3 \)[/tex]

d. A straight angle
A straight angle is another way of describing 180 degrees, which fits the previous calculation:
- Number of right angles needed: [tex]\( \frac{180}{90} = 2 \)[/tex]

### Summary
1. It is possible to form a non-identical quadrilateral like a parallelogram with the given sides of 6 and 3 units.
2. The side lengths 1, 2, and 4 cannot form a triangle.
3. The number of right angles required:
- 360 degrees: 4 right angles
- 180 degrees: 2 right angles
- 270 degrees: 3 right angles
- A straight angle (180 degrees): 2 right angles
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