Segment Addition Postulate Review

Front

Segment Addition Postulate in 'connect the dots' game with points A, B, C in a line, B between A and C.

Back

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

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.

Front

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?

Back

4

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.

Front

In a game of 'Connect the Dots', Arjun connects J to K (7 units), Harper connects K to L (9 units), and David connects J to L (16 units). Which statement is true?

Back

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

Answer explanation

JK + KL = JL, verifying Segment Addition Postulate.

Front

Find the value of y: N to M = 4y + 3, M to O = 5y - 2, N to O = 22.

Back

3

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.

Front

What is true about collinear points?

Back

Collinear points lie on the same line.

Answer explanation

Collinear points lie on the same line.

Front

The treasure is hidden at point C, between A and B. Distance A to C: 2x + 1 steps, C to B: 3x - 2 steps. Total A to B: 25 steps. Find x.

Back

6

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.

Front

Find the value of x given: E to F = 10 steps, E to G = 3x + 4 steps, F to G = x + 6 steps.

Back

5

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.

Front

What would Olivia, Scarlett, and Noah use the Segment Addition Postulate for on their treasure hunt map?

Back

Determining the length of the marked segment on the map.

Answer explanation

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

Front

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. What is the value of x?

Back

5

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.

Front

Under what condition can Kai, James, and Olivia be considered collinear when playing 'connect the dots' in the playground?

Back

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

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.'