Grade 7 Math, Page 69, Exercise 2 in Connecting Knowledge is an excellent Math resource for 7th-grade students and teachers. With detailed solutions for exercises 9.10, 9.11, 9.12 in the textbook on the topic of Triangle Side Relations, students can easily refer to and visualize problem-solving methods, enabling them to complete exercises quickly.
Explore more excellent Grade 7 Math resources:
- Solve Grade 7 Math in Connecting Knowledge with Life
- Solve Grade 7 Math, Page 83, Exercise 4 in Kite book: First Case of Triangle Congruence: Side - Side - Side
- Solve Grade 7 Math, Pages 46-47, Exercise 1 in Horizon of Creativity book: Angle and Side of a Triangle
Grade 7 Math, Page 69, Exercise 2: Connecting Knowledge with Life
Relationship between the three sides of a triangle
1. Solve Exercise 9.10 Page 69 Math Textbook Grade 7
Problem Statement: Given sets of three line segments with the following lengths:
a) 2 cm, 3 cm, 5 cm;
b) 3 cm, 4 cm, 6 cm;
c) 2 cm, 4 cm, 5 cm;
Which set cannot be the lengths of the three sides of a triangle? Why? For each remaining set, draw a triangle with the given side lengths.
Solution Guide: To check if three lengths can form the sides of a triangle, we only need to compare whether the longest length is less than the sum of the other two lengths, or if the shortest length is greater than the difference between the other two lengths.
Answer:
a) 2 cm + 3 cm = 5 cm (does not satisfy the triangle inequality). Thus, the set of line segments 2 cm, 3 cm, 5 cm is not the lengths of the three sides of a triangle.
b) 3 cm + 4 cm = 7 cm > 6 cm (satisfies the triangle inequality). Hence, the set of line segments 3 cm, 4 cm, 6 cm is the lengths of the three sides of a triangle.
c) 2 cm + 4 cm = 6 cm > 5 cm (satisfies the triangle inequality). Therefore, the set of line segments 2 cm, 4 cm, 5 cm is the lengths of the three sides of a triangle.
2. Solve Exercise 9.11 Page 69 Math Textbook Grade 7
Problem Statement: a) Given triangle ABC with AB = 1 cm and BC = 7 cm. Find the length of side CA, knowing it is an integer (cm).
b) Given triangle ABC with AB = 2 cm, BC = 6 cm, and BC as the longest side. Find the length of CA, knowing it is an integer (cm).
Solution Guide:
3. Solve Exercise 9.12 Page 69 Math Textbook Grade 7
Problem Statement: Given point M lies inside triangle ABC. Let N be the intersection point of line AM and side BC (H.9.18)
Solution Guide: In a triangle, the length of any side is always less than the sum of the lengths of the other two sides.
Answers:
Applying the triangle inequality to triangle MNB, we have:
Above is the guide to Solving math problems for grade 7 page 69 workbook 2, students can refer to Solving math problems for grade 7 page 71 workbook 2 and review Solving math problems for grade 7 page 65 workbook 2 to ensure understanding.
- Solving Math problems for grade 7 page 71 workbook 2 in Connect Knowledge - Concentrated exercises page 70
- Solving Math problems for grade 7 page 65 workbook 2 in Connect Knowledge - Exercise 32: Relationship of perpendicular lines and diagonals
Buzz
