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Solving Grade 7 math problems on page 58 of Workbook 1, book Connecting Knowledge with Life providing solutions for exercises 3.27, 3.28, 3.29, 3.30, 3.31 of the Focused Practice section. Students are encouraged to refer to these solutions to tackle similar exercises with ease and accuracy.
Explore various good Math 7 study materials:
- Solving Grade 7 Math problems, book Connecting Knowledge
- Solving Grade 7 Math problems on page 84 of Workbook 1, book Creative Horizon - Exercise 4: Theorem and proving a theorem
- Solving Grade 7 Math problems, book Connecting Knowledge
- Solving Grade 7 Math problems on page 84 of Workbook 1, book Creative Horizon - Exercise 4: Theorem and proving a theorem
- Solving Grade 7 math problems on page 87 of Workbook 1, book Kite - Chapter 3 review exercises
Problem 1: Solve Exercise 3.27 on Page 58 SGK Math Grade 7
Concentration Practice
1. Solve Exercise 3.27 on Page 58 SGK Math Grade 7
Given trapezoid ABCD with side AD perpendicular to both bases AB and CD. The angle measure at vertex B is twice the angle measure at vertex C. Find the measures of the angles of the trapezoid.
Solution Guide:
Using the property: If two parallel lines are intersected by a third line, then the corresponding angles are congruent.
Answer:
2. Solve Exercise 3.28 on Page 58 SGK Math Grade 7
Problem:
Solution Guide:
Draw the figure as requested in the problem.
The hypothesis is the given condition of the problem.
The conclusion is what needs to be proven.
Answer:
3. Solution to Problem 3.29 Page 58 Math Textbook Grade 7
Problem: Draw the bisectors Ax and By of an acute angle formed by line b perpendicular to two parallel lines c and d (H.3.48). Prove that these bisectors lie on two parallel lines.
Guide to solving: Use the signs to identify two parallel lines to prove.
Answer:
4. Solution to Problem 3.30 Page 58 Math Textbook Grade 7
Problem: Given two distinct lines a, b perpendicular to line c; d is another line perpendicular to a and distinct from c. Prove that:
a) a is parallel to b; b) c is parallel to d; c) b ⊥ d
Guide to solving:
We use the following theorem to prove:
+) Two distinct lines perpendicular to a third line are parallel to each other
+) If a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line.
Answer:
a) Since c is perpendicular to a and c is perpendicular to b, it follows that a is parallel to b (two lines perpendicular to a third line are parallel to each other).
b) Since a is perpendicular to c and a is perpendicular to d, it follows that c is parallel to d (two lines perpendicular to a third line are parallel to each other).
c) As b is perpendicular to c and c is parallel to d, b is perpendicular to c (a line perpendicular to one of two parallel lines is also perpendicular to the other line).
5. Solution to Exercise 3.31 on Page 58 of Grade 7 Math Textbook
Problem: Given Figure 3.49. Prove that:
a) Line d is parallel to BC.
b) Since d is perpendicular to AH.
c) Among the conclusions above, which conclusion can be inferred from the property of parallel lines, and which conclusion can be inferred from the sign of recognizing parallel lines?
Guidance for solution: Use the sign for recognizing parallel lines to prove.
Answer:
b) Because d is parallel to BC, and AH is perpendicular to BC, then d is perpendicular to AH (A line perpendicular to one of two parallel lines is also perpendicular to the other line).
c) Among the conclusions above, conclusion a) is inferred from the sign for recognizing parallel lines.
Conclusion b) is inferred from the property of parallel lines.
Here is the guidance for solving Grade 7 math problems on page 58, students, please refer to Grade 7 math problems on page 59 and review Grade 7 math problems on page 57 to solidify your knowledge.
- Solve Grade 7 math problems on page 57 in the book Connecting Knowledge - Exercise 11: Theorem and proof of theorem
- Solve Grade 7 math problems on page 59 in the book Connecting Knowledge - Exercise at the end of Chapter 3
