【People's Education Press】Junior High School Mathematics Grade 8 Part 1

This textbook is part of the compulsory education curriculum, designed for eighth-grade students in their first semester. The content covers the properties of triangles, criteria and properties of congruent triangles, axisymmetric figures, operations with polynomials including multiplication and factorization, and fundamental operations and equations involving rational expressions. The goal is to develop students' geometric logical reasoning abilities and algebraic computational skills.

Explore the beauty of geometric proofs, master the core of algebraic computation.

Author: Lin Qun

Acknowledgments: Approved by the Ministry of Education 2013, Second Prize in the National Excellent Textbook Award, First National Textbook Construction Award

1. Identification and Construction: Accurately identify and draw altitudes, medians, and angle bisectors of triangles; understand the concept of centroid.
2. Conceptual Analysis: Understand the stability of triangles and the instability of quadrilaterals, and explain their real-world applications.
3. Computation and Reasoning: Master the use of the triangle angle sum theorem and exterior angle properties for angle calculations; know the formulas for interior and exterior angles of polygons and solve practical polygon problems.
4. Master Concepts and Properties: Accurately identify corresponding vertices, sides, and angles of congruent triangles, and apply “corresponding sides are equal, corresponding angles are equal” in computations and proofs.
5. Master Criteria: Skillfully apply SSS and SAS to determine triangle congruence, and write formal proof processes.
6. Understand Logical Limits: Through exploration, recognize that SSA (side-side-angle) cannot be used as a criterion for congruence, fostering rigorous geometric logic.
7. Master Axis Symmetry Concept: Identify axisymmetric figures and accurately draw the symmetric image of a given figure about a specified line.
8. Deepen Understanding of Isosceles/Equilateral Triangles: Master the properties “equal sides imply equal angles” and “three lines coincide,” and use “equal angles imply equal sides” to identify isosceles triangles.
9. Computation and Proof: Apply the 30°-angle property of right triangles for length calculations, and understand the inequality relationship between larger sides and larger angles in triangles.
10. Proficiently Apply Exponent Rules: Accurately perform calculations using the rules for multiplying powers with the same base, power of a power, and power of a product.