Guidance on solving exercises 1, 2, 3 of question 3: Two parallel lines according to the curriculum in the document Solving 7th-grade math problems on page 104 of the Wings of Kite book. If you haven't solved the problem, you can refer to see how it's done, making it easier to do the exercises.
Referencing multiple good study materials for Grade 7 Mathematics
- Solving Grade 7 Math Problems with Wings of Kite Book
- Solving Grade 7 Math Problems on page 49 of the Connecting Knowledge Book - Exercise 9: Two parallel lines and signs of recognition
- Solving Grade 7 Math Problems on pages 80, 81 of the Creative Horizon Book - Exercise 3: Two parallel lines
Solving 7th-grade math problems on page 104 of the Wings of Kite book
Exercise 3. Two parallel lines
1. Solving Exercise 1 Page 104 of Math Textbook Grade 7
Problem: Observing Figure 44, knowing a // b.
Guidance on solving:
+ 1 line intersects 2 parallel lines creating pairs of alternate interior angles that are equal, congruent.
+ 2 vertical angles are equal.
+ 2 adjacent supplementary angles have a total measure of 180o.
Answer:
2. Solve Exercise 2 Page 104 Math Textbook Grade 7
Problem: Observe Figure 45.
a) Why are lines a and b parallel to each other?
b) Find the measure of angle BCD.
Guidance on solving:
+ Two adjacent supplementary angles have a total measure of 180 degrees.
+ If a line cuts two parallel lines creating either pairs of alternate interior angles that are equal or pairs of corresponding angles that are equal, then those two lines are parallel.
+ If a line cuts two parallel lines, then pairs of alternate interior angles are equal, pairs of corresponding angles are equal.
Answer:
3. Solve Exercise 3 Page 104 Math Textbook Grade 7
Problem: To ensure safety when moving on the staircase of a house, a handrail must be installed. Above the handrail is a banister serving as a support for convenient climbing up and down the stairs. Below the banister are parallel bars and parallel side bars. To ensure firmness, the banister's bars are fixed perpendicular to the stair steps.
In Figure 46, angle xOy equals How many degrees is the acute angle formed by a side bar with a vertical bar of the banister?
Guidance on solving:
+ Two adjacent supplementary angles have a total measure of 180 degrees.
+ If a line intersects two parallel lines, then pairs of alternate interior angles are equal, pairs of corresponding angles are equal.
Answer:
Let the intersection of the two side bars and the vertical bar be two points A and B.
Name the angles A1 and B1 (as shown in the diagram).
Because the vertical bar is perpendicular to the staircase step, the angle formed by the vertical bar and the staircase step is 90 degrees.
Then, the angle formed by the vertical bar and ray Oy is:
144o - 90o = 54o.
The side bar is parallel to ray Oy.
So, the measure of the angle formed by the vertical bar and ray Oy is equal to the measure of the angle formed by the side bar and the vertical bar (two corresponding angles).
Therefore, the acute angle formed by a side bar with a vertical bar of the banister is 54 degrees.
Exercise for Exercise 2: Two parallel lines have been guided to solve in the document Solving 7th-grade math problems on page 104 of the Wings of Kite book. If you want to see more solutions for the next lesson, you can check the link below.
- Solving Math 7 page 107 Workbook 1 Wings of Kite - Exercise 4. Theorem
- Solving Math 7 page 108 Workbook 1 Wings of Kite - Review exercises chapter 4
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