A triangle is a geometrical figure bounded by three straight lines and having three angles. Such a definition may be correct, but it gives one the idea that a triangle is a decidedly uninteresting figure. There are many different kinds of triangles and each one has its own interesting peculiarities.

**Bài viết liên quan:**

- Properties of triangles – Part 1
- Properties of triangles – Part 2
- Shapes vocabulary for math
- Vocabulary Angles
- Angle Practice 1

*From the information given, can you state the names *of these triangles?

1. I am readily suggested when you look at a trillium.

2. I appear when a man stands on level ground with his legs straight and his feet slightly apart.

3. I have a special name derived from a Greek word meaning “uneven.”

4. I am formed by joining the feet of the perpendiculars from the vertices of a triangle to the opposite sides.

5. The sum of the squares on two of my sides equals the square constructed on my third side.

6. There are at least two of us. We find that our corresponding angles are equal and our sides are proportional.

7. The sides and the diagonals of a quadrilateral are used to construct me.

8. My sides are not straight lines and the sum of my angles is greater than 180^{0}.

9. I have gained the title “pons asinorum” for a certain proposition in Euclid.

10. I am connected with the stars and the zenith.

Tóm tắt nội dung bài viết

**New vocabulary**

**geometric:** Hình học; **geometrical:** thuộc về hình học.

**bound:** Giới hạn, ranh giới, bao bởi.

**figure: **(toán học) Hình, con số.

**peculiarity:** Đặc thù, tính chất riêng.

**slightly:** Nhỏ, mỏng mảnh, yếu ớt.

**uneven:** (toán học) Lẻ (= odd).

**derive:** Xuất phát từ, bắt nguồn từ, lấy được từ,…

**perpendicular:** Góc vuông, đường vuông góc, mặt phẳng vuông góc, trực giao, thẳng đứng, thẳng góc.

**vertices**, số nhiều của **vertex: **(toán học) Đỉnh.

**proportional:** (toán học): Số hạng của tỷ lệ thức.

**diagonal: **Đường chéo, chéo.

**quadrilateral: **Hình bốn cạnh, hình tứ giác.

**angle: **Góc

**pons asinorum: **** Theo wiki** “In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the

*pons asinorum***“.**

**proposition:** (toán học) Sự trình bày một định lý hoặc vấn đề (có chứng minh); Định đề.

**zenith:** Điểm cao nhất, cực điểm.

** ****Answer key**

**1. EQUILATERAL (Đều)**

As the name suggests, all the sides are equal. Equilateral triangles have not only equal sides but have equal angles too and can thus be called equiangular triangles. The trillium has three axes of symmetry suggesting an equilateral triangle. Many plants have geometrical shapes in their roots, stems, leaves, and flowers. What shape is found in the cross-section of the stem of the sedge family?

**2. ****ISOSCELES (Cân)**

The word means “equal legs.” Any triangle which has two of its three sides equal is called an isosceles triangle. If we look around us we can often find geometrical figures in nature. In the construction of houses, ships, and aircraft, the isosceles triangle is often encountered.

** SCALENE (Thường)**

This is a triangle which is “uneven” because it has all its sides unequal. The word “scalene” has nothing to do with drawing to scale, but is derived from the Greek word “skalenos,” which means “uneven” or “unequal.”

**4. PEDAL (Thủy tức **hay **Thùy tức)**

This triangle is sometimes called the orthocentric triangle. If AD, BE, and CF are the perpendiculars dropped from the vertices of the triangle ABC to the opposite sides, then the

triangle DEF is the pedal triangle. The three perpendiculars pass through a common point called the orthocenter.

**5. RIGHT-ANGLED (Vuông)**

The unique property of the right-angled triangle ABC is that if angle A is the right angle then a^{2} = b^{2} + c^{2}. The geometrical proof of this property is associated with the Greek mathematician Pythagoras, who lived in the sixth century B.C. Triangles whose sides are in the ratios 3-4-5 or 5-12-13 are right-angled.

**6. SIMILAR (Đồng dạng)**

Two triangles are said to be similar if they have their angles equal to one another and have their sides, taken in order, about the corresponding equal angles proportional. The areas of similar triangles are proportional to the squares of their corresponding sides.

**7. HARMONIC** **(Điều hoà)**

ABCD is the quadrilateral and OXY is the harmonic triangle. It is formed by joining the intersection points of the sides and the intersection point of the diagonals.

**8. SPHERICAL**

A spherical triangle consists of a portion of a sphere bounded by three arcs of great circles. Obviously the sides do not consist of straight lines. The sum of the three angles of such a triangle lies between 180^{0} and 540^{0}. Much of the early work with spherical triangles was done by Menelaus about A.D. 100.

**9. ISOSCELES (Cân)**

The particular proposition proved that the angles at the base of an isosceles triangle are equal. The title “pons asinorum” means the “bridge of asses.” It is said that in the Middle Ages the “donkey” could not pass over this bridge to continue his study of Euclidean geometry, but the name may be due to the fact that the figure in Euclid resembles a simple truss bridge.

**10. ASTRONOMICAL**

This is a spherical triangle on a celestial sphere which has for its vertices the nearest celestial pole, the zenith, and the star under consideration.