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All exercises of Chapter III Final exercises are guided in the document Solving Grade 7 math problems on page 59, Exercise Book 1, Connecting Knowledge with Life Series. All solutions are explained in detail, students can easily understand and grasp effective problem-solving methods.
Referencing multiple good math learning resources for Grade 7
- Solving Grade 7 Math problems in Connecting Knowledge Book
- Solving Grade 7 math problems on pages 94, 95, Exercise Book 1, Kite Series - Exercise 1. Special Position Angles
- Solving Grade 7 math problems on pages 86, 87, Exercise Book 1, Horizon of Creativity Series - Final exercises of Chapter 4
Solving Grade 7 math problems on page 59, Exercise Book 1, Connecting Knowledge with Life Series
Final exercises of Chapter III
1. Solving Exercise 3.32 Page 59 Math Textbook Grade 7
Problem: Prove that: Given point A and line d, there is a unique line passing through A and perpendicular to d, meaning if there are two lines passing through A perpendicular to d, they must coincide.
Solution Guide:
Assume there are 2 lines passing through A perpendicular to d. We will prove that these 2 lines coincide.
Answer:
Suppose there are 2 lines a and a' passing through A and perpendicular to d.
Since a ⊥ d, and a' ⊥ d, then a // a' (two lines perpendicular to a third line are parallel to each other).
As A a, A a' ⇒ a ≡ a'.
There is only one line passing through A and perpendicular to d.
2. Solve Exercise 3.33 Page 59 Math Textbook Grade 7
Problem: Draw three distinct lines a, b, c such that a // b, b // c, and two distinct lines m, n are perpendicular to a. How many pairs of parallel lines are there on the figure, how many pairs of perpendicular lines?
Solution Guide:
+) If two lines are both perpendicular to a third line, they are parallel to each other.
+) A line perpendicular to one of two parallel lines is also perpendicular to the other line.
+) Two lines parallel to a third line are parallel to each other.
Answer:
We have:
+) Given a // b, b // c, hence a // c (Two lines parallel to a third line are parallel to each other).
+) Given m ⊥ a; n ⊥ a, thus m // n (Two lines perpendicular to a third line are parallel to each other).
According to the theorem 'A line perpendicular to one of two parallel lines is also perpendicular to the other line,' we have:
+) a is parallel to b; a is perpendicular to n so b is perpendicular to n.
+) a is parallel to b; a is perpendicular to m so b is perpendicular to m.
+) a is parallel to c; a is perpendicular to n so c is perpendicular to n.
+) a is parallel to c; a is perpendicular to m so c is perpendicular to m.
There are 4 pairs of parallel lines: a // b ; a // c ; b // c; m // n.
There are 5 pairs of perpendicular lines: b ⊥ n; b ⊥ m; c ⊥ n; c ⊥ m; a ⊥ n; a ⊥ m.
3. Solving Exercise 3.34 Page 59 Math Textbook Grade 7
Solution Guide:
Draw the line passing through C and parallel to Ax.
Use the property of parallel lines to prove.
Answer:
Draw line d through C and parallel to Ax.
Draw line d through C and parallel to Ax.
4. Solving Exercise 3.35 Page 59 Math Textbook Grade 7
Problem: Given figure 3.51, where Ox and Ox' are two opposite rays.
Solution Guide:
The sum of measures of two adjacent supplementary angles is 180 degrees.
Answer:
5. Solving Exercise 3.36 Page 59 Math Textbook Grade 7
Solution Guide:
Draw the opposite ray of ray Oy.
Two adjacent angles supplementary have a sum of measures equal to 180 degrees.
Answer:
Draw ray Ot as the opposite ray of ray Oy.
Here is the solution guide for Grade 7 math problem on page 59 exercise book 1. Students should refer to Grade 7 math problem on page 62 exercise book 1 and review Grade 7 math problem on page 58 exercise book 1 to solidify their understanding.
- Solving Grade 7 math problem on page 58 exercise book 1, Connecting Knowledge Series - Focused practice page 58
- Solving Grade 7 math problem on page 62 exercise book 1, Connecting Knowledge Series - Exercise 12: Sum of angles in a triangle
