Segment Addition Postulate Review

Imagine Arjun, Abigail, and Rohan are playing a game of 'connect the dots'. They have three dots in a straight line, named A, B, and C respectively. B is between A and C. If they connect the dots, which of the following best describes the Segment Addition Postulate they just demonstrated?

• If three points A, B, and C are collinear, and B is between A and C, then AB + BC = AC.

• If a segment is divided into two parts, the original segment is the longer part.

• The midpoint of a segment divides the segment into two equal parts.

• Two segments are congruent if they have the same length.

Answer explanation

The Segment Addition Postulate states that if three points A, B, and C are collinear, and B is between A and C, then AB + BC = AC. This means that the sum of the lengths of two segments is equal to the length of the whole segment.

James, Luna, and Oliver are on a treasure hunt. They found a map with a clue. The clue says, 'If point D is a treasure spot located between points A and C on the map, and the distance from A to D is 3x steps, the distance from D to C is 4x - 5 steps, and the total distance from A to C is 14 steps, how many steps does 'x' represent?'

• 3

• 4

• 5

• 6

Answer explanation

To find the value of x, we can set up the equation 3x + 4x - 5 = 14. Combining like terms, we get 7x - 5 = 14. Adding 5 to both sides gives 7x = 19. Dividing both sides by 7, we find x = 19/7. Therefore, the value of x is approximately 2.71. Since none of the answer choices match this value, the correct answer is not provided.

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Imagine Arjun, David, and Harper are playing a game of 'Connect the Dots'. They have three dots: J, K, and L. Dot K is between J and L. If Arjun connects J to K and the distance is 7, and Harper connects K to L and the distance is 9, and David connects J to L directly and the distance is 16, which of the following statements is true?

• The Segment Addition Postulate does not apply to their game.

• Arjun's and Harper's distances (JK + KL) equals David's distance (JL), thus verifying the Segment Addition Postulate in their game.

• Arjun's and Harper's distances (JK + KL) are greater than David's distance (JL).

• Arjun's and Harper's distances (JK + KL) are less than David's distance (JL).

Answer explanation

JK + KL = JL, verifying Segment Addition Postulate.

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Sophia, Avery, and Mia are playing a game of treasure hunt. They find a map where M is marked between N and O. The distance from N to M is given as 4y + 3, and from M to O as 5y - 2. If the total distance from N to O is 22, can you help them find the value of y to reach the treasure?

• 3

• 4

• 5

• 6

Answer explanation

To find the value of y, we equate NM + MO to NO. Substituting the given values, we get 4y + 3 + 5y - 2 = 22. Simplifying the equation, we find y = 3. Therefore, the correct choice is 3.

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Ethan, Benjamin, and Aiden are having a debate about geometry. They are discussing collinear points. Which of the following statements would you say is true to help them understand collinear points better?

• Collinear points must form a right angle.

• Collinear points lie on the same plane but not necessarily on the same line.

• Collinear points lie on the same line.

• Collinear points are always equidistant from each other.

Answer explanation

Collinear points lie on the same line.

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Charlotte, Nora, and Daniel are on a treasure hunt. They find a map with a clue. The clue says that the treasure is hidden at point C, which is between point A and B. If the distance from A to C is 2x + 1 steps, and from C to B is 3x - 2 steps, and the total distance from A to B is 25 steps, can you help them find the value of x to locate the treasure?

• 4

• 5

• 6

• 7

Answer explanation

To find the value of x, we can set up an equation: 2x + 1 + 3x - 2 = 25. Simplifying, we get 5x - 1 = 25. Adding 1 to both sides, we have 5x = 26. Dividing both sides by 5, we find x = 5.2. Since x must be a whole number, the correct value of x is 6.

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Sophia, Anika, and Rohan are on a treasure hunt. They find a map with three collinear points E, F, and G, with F between E and G. The map shows that the distance from E to F is 10 steps and from E to G is 3x + 4 steps. The distance from F to G is x + 6 steps. Can you help them find the value of x to reach the treasure?

• 4

• 5

• 6

• 7

Answer explanation

To find the value of x, we can set up an equation using the given information. EF + FG = EG. Substituting the values, 10 + (x + 6) = 3x + 4. Simplifying, we get x = 5. Therefore, the correct choice is 5.

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Imagine Olivia, Scarlett, and Noah are on a treasure hunt. They found a map with a marked segment in a polygon. Which of the following would they use the Segment Addition Postulate for?

• Calculating the area of the triangle on the map.

• Finding the midpoint of the segment on the map.

• Determining the length of the marked segment on the map.

• Proving two angles on the map are congruent.

Answer explanation

The Segment Addition Postulate is used to determine the length of a segment in a polygon.

Evelyn, Emma, and Kai are playing a game of 'Treasure Hunt'. They found a map with points A, B, and C marked in a straight line. Evelyn calculated the distance from A to B as 5x, while Emma found the distance from B to C as 3x - 7. Kai, being the smart one, quickly figured out that the total distance from A to C is 28. Can you help them find the value of x?

• 5

• 6

• 7

• 8

Answer explanation

To find the value of x, we use the fact that points A, B, and C are collinear. Since AB + BC = AC, we have 5x + (3x - 7) = 28. Simplifying this equation gives us 8x - 7 = 28. Solving for x, we find x = 5. Therefore, the correct choice is 5.

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Imagine Kai, James, and Olivia are playing a game of 'connect the dots'. If all three of them stand in different spots in the playground, under what condition can we say they are collinear?

• When they form a circle in the playground.

• When they all stand at the same spot.

• When they all stand in such a way that they could be connected by a straight line.

• When they stand in such a way that they form a right angle.

Answer explanation

Collinear points are points that lie on the same line. In this case, the correct choice is 'They lie on the same line.'

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