The term that best describes segment \( QC \) is angle bisector. This is because segment \( QC \) divides the angle formed by lines \( QP \) and \( QR \) into two equal angles, which is the definition of an angle bisector.
Use the image to answer the question. Arttu followed the following instructions: Draw an angle using a straightedge with vertex point Q . Place points P and R at the end of the angle forming segments QP¯¯¯¯¯¯¯¯ and QR¯¯¯¯¯¯¯¯ . Using a compass, draw an arc that intersects both sides of the angle. Place two points, A and B , at the intersection of the arc with both sides of the angle. Placing the pointed end of the compass on point A , draw a smaller arc inside the angle that extends more than halfway across the inside of the angle. Placing the pointed end of the compass on point B , draw a smaller arc inside the angle that extends more than halfway across the inside of the angle. Place point C at the intersection of the two smaller arcs and draw a segment from the vertex point Q to point C . What term best describes segment QC¯¯¯¯¯¯¯¯ ? (1 point) Responses midpoint midpoint angle bisector angle bisector an arc an arc segment bisector segment bisector Skip to navigation
11 answers
Carlos constructed the angle bisector of ∠JKI by constructing ray KM . Carlos then constructed the angle bisector of ∠MKI by constructing ray KN . If the measurement of ∠JKI is 56 degrees, what is the measurement of ∠NKI ?(1 point) Responses The measurement of ∠NKI is 28 degrees. The measurement of angle upper N upper K upper I is 28 degrees. The measurement of ∠NKI is 112 degrees. The measurement of angle upper N upper K upper I is 112 degrees. The measurement of ∠NKI is 7 degrees. The measurement of angle upper N upper K upper I is 7 degrees. The measurement of ∠NKI is 14 degrees
To find the measurement of \( \angle NKI \), we can break it down step-by-step based on the given information.
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Carlos constructed the angle bisector of \( \angle JKI \), which measures 56 degrees. When he bisects this angle by constructing ray \( KM \), the two resulting angles are: \[ \angle JKM = \angle M KI = \frac{56}{2} = 28 \text{ degrees} \]
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Carlos then constructs the angle bisector of \( \angle M KI \) using ray \( KN \). Since \( \angle M KI \) measures 28 degrees, when he bisects this angle, the two resulting angles are: \[ \angle MK N = \angle NKI = \frac{28}{2} = 14 \text{ degrees} \]
Thus, the measurement of \( \angle NKI \) is 14 degrees.
Therefore, the correct response is The measurement of \( \angle NKI \) is 14 degrees.
Use the images to answer the question. Step 1: Step 2: Step 3: Step 4: Determine the type of construction being done from the steps shown. (1 point) Responses perpendicular lines perpendicular lines angle bisector angle bisector parallel lines through a point not on the given line parallel lines through a point not on the given line perpendicular bisector
To accurately determine the type of construction based on the steps provided, I would need to visualize the images involved in the construction. However, from your descriptions of the options provided, I can guide you on how to identify the construction type based on common methods:
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Perpendicular Lines: If the construction involves drawing a line that intersects another line at a 90-degree angle.
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Angle Bisector: This involves splitting an angle into two equal angles.
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Parallel Lines Through a Point Not on the Given Line: This usually involves using a compass and straightedge to ensure a line is equidistant from another line, which requires drawing from a point not on the original line.
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Perpendicular Bisector: This is constructing a line that divides another line segment into two equal parts at a right angle.
If you can describe the steps or provide more details about the construction, I can help to identify it more clearly. For example, if the process involved creating equal angles or segments, it would indicate an angle bisector or perpendicular bisector, respectively.
Based on the standard constructions, please select the option that corresponds to the descriptions of the steps you see in the images.
Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point) Responses 18, 11, 8 18, 11, 8 9, 17, 11 9, 17, 11 11, 19, 9 11, 19, 9 18, 10, 8
To determine whether a set of side lengths can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that for any three lengths \( a \), \( b \), and \( c \) to form a triangle, the following conditions must be met:
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
We can apply these conditions to each set of lengths provided:
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Set: 18, 11, 8
- \( 18 + 11 = 29 > 8 \) (True)
- \( 18 + 8 = 26 > 11 \) (True)
- \( 11 + 8 = 19 > 18 \) (False)
- This set does not form a triangle.
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Set: 9, 17, 11
- \( 9 + 17 = 26 > 11 \) (True)
- \( 9 + 11 = 20 > 17 \) (True)
- \( 17 + 11 = 28 > 9 \) (True)
- This set forms a triangle.
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Set: 11, 19, 9
- \( 11 + 19 = 30 > 9 \) (True)
- \( 11 + 9 = 20 > 19 \) (True)
- \( 19 + 9 = 28 > 11 \) (True)
- This set forms a triangle.
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Set: 18, 10, 8
- \( 18 + 10 = 28 > 8 \) (True)
- \( 18 + 8 = 26 > 10 \) (True)
- \( 10 + 8 = 18 = 18 \) (Not Greater)
- This set does not form a triangle.
The sets that do not form a triangle based on the Triangle Inequality Theorem are:
- 18, 11, 8
- 18, 10, 8
However, since the question asks for the option that does not form a triangle, the first option provided, 18, 11, 8, would be the most direct answer.
So the final answer is: 18, 11, 8.
Use the image to answer the question. The diagram shows the distance between your house, the bank, and the farmer’s market. You need to stop at the bank before going to the farmer’s market. Given the information in the diagram, identify which statement is true. (1 point) Responses The distance from your house to the bank and then the farmer’s market is 8 miles. The distance from your house to the bank and then the farmer’s market is 8 miles. The distance from your house to the bank and then the farmer’s market is less than 5 miles. The distance from your house to the bank and then the farmer’s market is less than 5 miles. The distance from your house to the bank and then the farmer’s market is greater than 5 miles. The distance from your house to the bank and then the farmer’s market is greater than 5 miles. The distance from your house to the bank and then the farmer’s market is equal to 5 miles.
To determine the correct statement regarding the distances between your house, the bank, and the farmer's market, we would generally rely on the information typically present in the diagram. Since I cannot see the image to gather specific distances, let's analyze the statements based purely on their logical implications.
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The distance from your house to the bank and then the farmer’s market is 8 miles.
- This statement asserts a specific distance.
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The distance from your house to the bank and then the farmer’s market is less than 5 miles.
- This would mean the combined distance is significantly short for typical distances in a neighborhood.
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The distance from your house to the bank and then the farmer’s market is greater than 5 miles.
- This means the total distance is longer than 5 miles.
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The distance from your house to the bank and then the farmer’s market is equal to 5 miles.
- This would indicate a specific average distance often found in a certain setting.
Without access to the diagram, we can't ascertain which is mathematically true, but based on typical urban distances, it might be more likely for either the 8-mile or the greater than 5-mile statements to hold true.
If the distance indications in the diagram suggest that the combined journey is quite common (assuming the locations aren't too far), then the greater than 5 miles choice seems reasonable.
If you can recall or provide specific distances from the diagram, I can help fine-tune which response accurately reflects that information. Based on common scenarios in distance and urban travel, I would lean towards the option "The distance from your house to the bank and then the farmer’s market is greater than 5 miles." if that's consistent with what you've seen.
In 1–2 sentences, define parallel and perpendicular lines and explain the difference between the two.(2 points)
Parallel lines are lines in a plane that never intersect and are always equidistant from each other, maintaining the same slope. Perpendicular lines, on the other hand, intersect at a right angle (90 degrees). The key difference is that parallel lines do not meet at any point, while perpendicular lines intersect each other at a specific angle.