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Math Grade 7 Exercise 84 Workbook 1 Creative Horizon Book: Principle and Proof of a Principle detailed solution guide for exercises 1, 2, 3, 4, 5 in Textbook. Students can refer to understand and solve exercises easily and accurately.
Refer to additional Math 7 learning materials:
- Complete set Math Grade 7 Creative Horizon Book Solutions
- Math Grade 7 Exercise 87 Workbook 1 Kite - Chapter 3 review exercises
- Complete set Math Grade 7 Creative Horizon Book Solutions
- Math Grade 7 Exercise 87 Workbook 1 Kite - Chapter 3 review exercises
- Math Grade 7 Exercise 58 Workbook 1 Knowledge Connection - Concentrated practice page 58
Solving exercise on page 84 of Textbook 1, Horizon of Creativity book
Statement and proof of a theorem
1. Solving Exercise 1 on Page 84 of Math Textbook Grade 7
Problem: Draw a figure, write hypothesis, conclusion of the theorem: 'A line perpendicular to one of two parallel lines is also perpendicular to the other line'.
Guidance for solution:
The hypothesis represents the given conditions in the problem.
The conclusion is what needs to be proven.
Using the property: If a line intersects two parallel lines then:
Two alternate interior angles are congruent.
Two corresponding angles are congruent.
Answer:
2. Solving Exercise 2 on Page 84 of Math Textbook Grade 7
Problem: State the missing part of the following conclusion:
a) If a line intersects two parallel lines then the two alternate interior angles .?...
b) If two distinct lines are perpendicular to a third line then .?..
Guidance for solution:
a) Property of two parallel lines
b) Signs to recognize two parallel lines
Answer:
a) If a line intersects two parallel lines then the two alternate interior angles are equal (Property of two parallel lines).
b) If two distinct lines are perpendicular to a third line then they are parallel to each other (Signs to recognize two parallel lines).
3. Solving Exercise 3 on Page 84 of Math Textbook Grade 7
Problem: State the missing part of the following conclusion:
a) If a line intersects two lines such that it forms a pair of alternate interior angles .?...then those lines are parallel.
b) If two distinct lines are ..?.. to a third line then they are parallel to each other
Guidance for solution:
Signs to recognize two parallel lines.
Answer:
a) If a line intersects two lines such that it forms a pair of alternate interior angles equal then those lines are parallel. (Signs to recognize two parallel lines)
b) If two distinct lines are perpendicular to a third line then they are parallel to each other.
4. Solving Exercise 4 on Page 84 of Math Textbook Grade 7
Problem: State the theorem about two distinct lines that are parallel to a third line.
Guidance for solution:
Draw the figure, state the theorem.
Answer:
Two distinct lines parallel to a third line are parallel to each other.
5. Solving Exercise 5 on Page 84 of Math Textbook Grade 7
Problem: We call two angles whose sum is 90° complementary angles. Write the hypothesis, conclusion in symbols and prove the theorem: 'If two angles are complementary to the same angle, then they are equal'.
Guidance for solution:
The hypothesis represents the given conditions in the problem.
Conclusion is what needs to be proven.
Answer:
Here's the guidance for Solving Math Problems Grade 7 page 84 exercise 1, students please refer to the solution to Math Problems Grade 7 page 86, 87 exercise 1 and review solving Math Problems Grade 7 page 80, 81 exercise 1 to solidify your knowledge.
- Solving Math Problems Grade 7 page 86, 87 exercise 1 in the Horizon of Creativity Book - Final exercises of Chapter 4
- Solving Math Problems Grade 7 page 93, 94, 95 exercise 1 in the Horizon of Creativity Book - Exercise 1: Data Collection and Classification
