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Quick guide to solving 6th-grade math exercises on pages 112, 113, 114 (Concise)
1. Solve 6th-grade math exercises page 112, 113, 114 exercise 22
Complete the blanks in the following statements:
a) The figure formed by point O and a part of the line divided by point O is called a …
b) Any point R lying on the line xy is the common vertex of …
c) If point A is between two points B and C, then:
– Two rays … are opposite.
– Rays CA and … coincide.
– Rays BA and BC are ….
Solution:
a) ray with origin O
b) two opposite rays Rx and Ry
c) If point A is between two points B and C, then:
– AB and AC
– CA and CB
– BA and BC
2. Solve 6th-grade math exercises page 112, 113, 114 exercise 23
On line A, four points M, N, P, Q are given as shown in figure 31. Answer the following questions:
a) In rays MN, MP, MQ, NP, NQ, which rays coincide?
b) In rays MN, NM, MP, which rays are opposite?
c) Name two opposite rays with vertex P.
Solution:
a) Rays that coincide are:
- MN, MP, MQ with vertex M
- NP, NQ with vertex N
b) There are no opposite rays
c) Two opposite rays with vertex P are rays PQ and PN or PQ and PM.
3. Solve 6th-grade math exercises page 112, 113, 114 exercise 24
Given two opposite rays Ox, Oy with point A on ray Ox, points B and C on ray Oy (B between O and C). Name:
a) The ray coinciding with BC
b) The ray opposite to BC.
Solution:
We have the illustration
a) The ray coinciding with ray BC is ray By.
b) The ray opposite to ray BC is ray BO, ray BA, or ray Bx (these three rays coincide)
4. Solve 6th-grade math exercises page 112, 113 exercise 25
Given two points A and B, draw:
a) The line AB
b) The ray AB.
c) The ray BA.
Solution:
We have the illustration
5. Solve 6th-grade math exercises page 112, 113, 114 exercise 26
Draw ray AB. Take point M on ray AB, ask:
a) Are points B and M on the same side with respect to point A or on the opposite side with respect to point A?
b) Is point M between points A and B or is point B between points A and M?
Solution:
The illustration is as follows:
- Case 1: Point M is between points A and B
- Case 2: Point M is not between points A and B
a) In both cases, points B and M are on the same side as point A.
b)
- Case 1: Point M is between A and B
- Case 2: Point B is between A and M
6. Solve 6th-grade math exercises page 113 exercise 27
Fill in the blanks in the following statements:
a) Ray AB is a figure including point A and all points on the same side with respect to B for …
b) The figure formed by point A and the line segment containing all points on the same side with respect to A is a ray with vertex …
Solution:
a) A
b) A
7. Solve 6th-grade math exercises page 113 114 exercise 28
Draw the line xy. Take point O on the line xy. Take point M on ray Oy. Take point N on ray Ox.
a) Write the names of two rays opposite at O
b) Among the three points M, O, N, which point is between the other two?
Solution:
We have the illustration
a) Rays Ox and Oy are two rays opposite at O
b) Among the three points M, O, N, point O is between the other two.
8. Solve 6th-grade math exercises page 112, 113, 114 exercise 29
Given two opposite rays AB and AC
a) Let M be a point on ray AB. Among the three points M, A, C, which point is between the other two?
b) Let N be a point on ray AC. Among the three points N, A, B, which point is between the other two?
Solution:
We have the illustration
a) Point A is between the other two points in the three points M, A, C
b) Point A is between the other two points in the three points N, A, B
9. Solve 6th-grade math exercises page 114 exercise 30
Fill in the blanks in the following statements:
If point O lies on line xy, then:
a) Point O is the common vertex of …
b) Point … is between any other point different from O on ray Ox and any other point different from O on ray Oy.
Solution:
a) two opposite rays Ox and Oy
b) O
10. Solve 6th-grade math exercises page 112, 113, 114 ray exercise 31
Take 3 non-collinear points A, B, C and draw two rays AB, AC:
a) Draw ray Ax intersecting line BC at M between points B and C.
b) Draw ray Ay intersecting line BC at N not between points B and C.
Solution:
Take three non-collinear points A, B, C. Draw two rays AB and AC
a) Draw ray Ax intersecting line BC at M between points B and C
b) Draw ray Ay intersecting line BC at N not between points B and C
11. Solve 6th-grade math exercises page 114 exercise 32
In the following statements, choose the correct one:
a) Two rays Ox and Oy sharing the same origin are opposite.
b) Two rays Ox and Oy lying on the same line are opposite.
c) Two rays Ox and Oy forming the line xy are opposite.
Solution:
The correct statement is c) Two rays Ox and Oy forming the line xy are opposite.
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Math solving materials for 6th-grade page 112, 113, 114 include concepts about Rays, what are opposite rays, and coincident rays with specific notes along with detailed solutions, helping students grasp multiple study methods and improve math learning outcomes. Next, students can review the previously solved 6th-grade math exercises page 109, 110 or preview the upcoming 6th-grade math exercises page 115, 116 for better learning in Math class.
