Sure! Let’s go through the questions one by one.
Question 1
Frankie constructed segment \( \overline{AB} \) using a compass and a straightedge. He then placed point C so that it is not on the segment he constructed.
Response: The next step Frankie must take to construct a copy of \( \overline{AB} \) using point C as one of the endpoints is:
- Use a compass, measure the distance between points A and B.
This will allow him to replicate the length of \( \overline{AB} \) starting from point C.
Question 2
Sally constructed angle \( \angle AOB \) with \( \overline{OC} \) as an angle bisector. Given that the measure of \( \angle AOB \) is 84 degrees, we need to find the measure of \( \angle AOC \).
Response: Since \( \overline{OC} \) is the angle bisector:
- Measure of \( \angle AOC = \frac{1}{2} \times \text{measure of } \angle AOB = \frac{1}{2} \times 84^\circ = 42^\circ. \)
So, the correct answer is:
- 42°
Question 3
This question requires showing all work which typically involves calculations or specific instructions. If you have a specific problem or example you would like to solve, please provide it, and I’d be happy to assist!
Question 4
Regarding the slopes of parallel lines:
Response: The correct statement is:
- Parallel lines have the same slope.
This is because for two lines to be parallel, they must never intersect, which occurs when they have identical slopes.
Question 5
If a triangle has two sides measuring 8 cm and 12 cm, we need to find a possible length for the third side. We'll use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
- \( x + 8 > 12 \) → \( x > 4 \)
- \( x + 12 > 8 \) → \( x > -4 \) (always true)
- \( 8 + 12 > x \) → \( 20 > x \) or \( x < 20 \)
Putting these together:
- \( 4 < x < 20 \)
The only option from the provided responses that fits this range is 5 cm and 3 cm options.
Response:
- The third side could be: 5 cm (valid)
- The option 3 cm is invalid (since 3 < 4).
Question 6
Similar to Question 3, to earn credit, this question requires showing all work. Please clarify if there's a specific problem you need help with, and I can guide you through the solution!