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Exercises on Principles and proving Principles are all guided in the document Solving Math for 7th Grade Page 57 Workbook 1 Connect Knowledge Series, let's refer to it to compare with the solutions as well as grasp the knowledge of the lesson most effectively.
Refer to other Math solving materials:
- See the complete set of Solving Math for 7th Grade Connect Knowledge Series
- Solving Math for 7th Grade Page 85, 86 Workbook 1 Kite - Exercise 2. Triangular prism. Quadrilateral prism
- Solving Math for 7th Grade Page 80, 81 Workbook 1 Horizon of Creation - Exercise 3: Two parallel lines
Solving Math for 7th Grade Page 57 Workbook 1 Connect Knowledge Series
Principles and proving Principles
1. Solve Exercise 3.24 Page 57 Math Textbook Grade 7
Problem: Can the principle: 'Two lines perpendicular to a third line are parallel to each other' be directly deduced from the principle about the sign of parallel lines? How is it deduced?
Solution guide:
Using the signs identifying parallel lines to answer the question.
Answer:
Suppose there are 2 distinct lines a, b both perpendicular to a line c.
Thus, the above principle can be directly deduced from the principle about the signs identifying parallel lines.
2. Solve Exercise 3.25 Page 57 Math Textbook Grade 7
Problem: Prove the principle stated in Example on page 56: 'A line perpendicular to one of two parallel lines is also perpendicular to the other line'. In that proof, what known truths did we use?
Solution guide:
Using the property: If a line intersects two parallel lines then:
Two congruent angles are equal
Two corresponding angles are equal
Answer:
Let's assume there are 2 parallel lines a and b, line c is perpendicular to a. We must prove that c is also perpendicular to b.
Indeed,
In the proof above, we utilized the property of two parallel lines.
3. Solve Exercise 3.26 Page 57 Math Textbook Grade 7
Problem: Given angle xOy is not a straight angle. Which of the following statements is true?
If there's an assertion that is incorrect, provide an example showing that it's incorrect.
(Hint: Consider the ray opposite to a bisector ray)
Solution guide:
Use the definition of an angle bisector ray to conclude.
Answer:
Assertion (1) is correct.
Assertion (2) is incorrect because:
With the workbook Solving Math for 7th Grade Page 57 Connect Knowledge Series, you can easily and accurately solve exercises on Principles and proving Principles.
Next exercises:
- Solve Math for 7th Grade Page 58 Workbook 1 Connect Knowledge Series - Focus exercises on page 58
- Solve Math for 7th Grade Page 59 Workbook 1 Connect Knowledge Series - Exercises at the end of chapter 3
