“It is better to learn from friends than from a teacher,” as the old proverb goes. But what if you encounter a difficult problem and no one is around? At this moment, the key lies within yourself, in your perseverance and thirst for knowledge. And today, “HOC LAM” will help you “crack” exercise 12 of the 8th-grade geometry textbook on page 74, empowering you to confidently conquer knowledge and achieve high scores in your studies.
Exercise 12 Geometry Grade 8 Textbook Page 74: Unveiling the Secrets
Exercise 12 on page 74 of the 8th-grade Geometry textbook is a problem about the properties of trapezoids, a topic that seems simple but contains many “pitfalls” for students.
Analyzing the Problem: Grasping the “Essence”
The exercise requires you to prove an important property of trapezoids: The sum of two angles adjacent to a leg of a trapezoid is 180 degrees.
To solve this problem, we need to analyze the elements:
- Trapezoid: A quadrilateral with two parallel opposite sides.
- Angles adjacent to a leg: Two angles next to each other and sharing a common leg of the trapezoid.
How to Solve Exercise 12 Geometry Grade 8 Textbook Page 74: Step-by-Step “Cracking”
To prove that the sum of two angles adjacent to a leg of a trapezoid is 180 degrees, we will use knowledge of corresponding angles, consecutive interior angles, and properties of parallel lines.
Step 1: Draw trapezoid ABCD (AB // CD).
Step 2: Draw a line through A parallel to BC, intersecting CD at E.
Step 3: Proof:
- Angle A + Angle D = 180 degrees: Because Angle A and Angle D are consecutive interior angles of two parallel lines AB and CD.
- Angle B + Angle C = 180 degrees: Because Angle B and Angle C are consecutive interior angles of two parallel lines AD and BC.
Step 4: Conclusion: The sum of two angles adjacent to a leg of a trapezoid is 180 degrees.
Note: You can apply this solution to both isosceles and scalene trapezoids.
Frequently Asked Questions About Exercise 12: Answering Your Queries
- Why draw an additional parallel line? Drawing an additional parallel line is to create pairs of corresponding angles and consecutive interior angles to apply the properties of parallel lines, thereby deducing that the sum of two angles adjacent to a leg is 180 degrees.
- Is there another way to solve this problem? Besides the above method, you can use knowledge of exterior angles of a triangle or properties of two perpendicular lines.
- How to memorize knowledge about trapezoids? You should review the properties of trapezoids, classify common types of exercises, and practice a lot to master the knowledge.
Spiritual Perspective on Exercise 12: “Learning is the Path to Cultivating the Mind”
According to Vietnamese spiritual beliefs, learning is the path to cultivating the mind, helping people enhance their bravery and wisdom. Exercise 12 of the 8th-grade geometry textbook on page 74 is not just a difficult math problem, but also a lesson in perseverance, thirst for knowledge, and effort to overcome challenges.
Remember that knowledge is infinite, always maintain an attitude of curiosity, eagerness to learn, and willingness to overcome difficulties. This will help you achieve success in your studies and life.
Diagram of a trapezoid labeled ABCD, illustrating properties from the Grade 8 geometry textbook.
“HOC LAM” – Always By Your Side on Your Learning Journey
Do you need more support with exercise 12 or other exercises in the 8th-grade Geometry textbook? Contact “HOC LAM” at 0372888889 or visit us directly at 335 Nguyen Trai, Thanh Xuan, Hanoi. We are always ready to accompany you on your journey to conquer knowledge!
Note: This article is for reference purposes, helping you better understand exercise 12 of the 8th-grade geometry textbook on page 74. To achieve the best learning results, you should also refer to textbooks, reference books, and ask your teachers for advice.
