Lesson 5.5 · Classification of triangles
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 118–120).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Classify triangles as acute-, right-, or obtuse-angled.
- 02Identify isosceles and equilateral triangles and their symmetry.
- 03Count equilateral triangles hidden in a diagram.
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.G.A.1 | Understand shared attributes of shapes. |
| 4.G.A.2 | *(preview)* Classify figures; lines of symmetry. |
| 4.G.A.3 | *(preview)* Line symmetry. |
| 3.G.A.1 | Shared attributes. |
Eureka Math Correspondence
| Shanghai Maths | Focus | Eureka Math |
|---|---|---|
| Triangles | Classify by angles/sides | G4 M4 preview |
Core Concepts
Sort triangles by angles and by sides; connect to symmetry.
By Angles
Acute-angled
All angles acute.
Right-angled
One right angle.
Obtuse-angled
One obtuse angle.
By Sides
Isosceles: at least two equal sides. Equilateral: all sides equal (also equiangular).
Draw & Count
Draw isosceles/equilateral with lines of symmetry; count equilateral triangles in a figure.
Key Terms & Definitions (Reference)
Quick glossary for this lesson.
| Term | Definition |
|---|---|
| Isosceles triangle | At least two sides equal. |
| Equilateral triangle | All three sides equal. |
| Acute / right / obtuse-angled | Classified by greatest angle. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Acute $1,3,5,10$; right $2,4,7,8$; obtuse $6,9$; isosceles $5,7,9,10$; equilateral $5$.
2. isosceles; equilateral · regular; $1$; $3$; special; acute-angled.
3–4. Draw / label parts (legs, base, vertex angle, base angles).
5. MC — D.
6. 3 triangles to centre; join midpoints → 4 equilateral.
7–8. $27$ equilateral; $19$ isosceles ($7$ equilateral); pentagram $35$ isosceles.