**Các thuộc tính của tam giác – Phần 2**

**similar: **Đồng dạng

**congruent:** Tương đẳng

**median:** Đường trung tuyến

**vertex:** Đỉnh (số ít), vertices (số nhiều)

**midpoint:** Điểm giữa.

**opposite side:** Cạnh đối diện

**cross:** Cắt nhau, giao nhau, đi qua

**angle bisectors:** Các góc phân giác

**center:** Tâm

**inscribed:** Nội tiếp

**circumscribed:** Ngoại tiếp

**altitude:** Độ cao, đường cao

**perpendicular bisectors:** Đường trung trực

**inequality:** Bất đẳng thức

BÀI VIẾT LIÊN QUAN:

- Calculating with triangles
- Properties of triangles – Part 1
- The name of all triangles
- Vocabulary angles
- Angles practice 1

**Similar triangles**

Two triangles are said to be *similar *(having the same
shape) if their corresponding angles are equal. The sides of similar triangles
are in the same proportion. The two triangles below are similar because they
have the same corresponding angles.

*a : d = b : e = c : f*

**Example:**

Two triangles both have angles of 30°, 70°, and 80°. If the sides of the triangles are as indicated below, find the length of side x.

**Congruent triangles**

Two triangles are *congruent *(*identical *in
shape and size) if any one of the following conditions is met:

1. Each side of the first triangle equals the corresponding side of the second triangle.

2. Two sides of the first triangle equal the corresponding sides of the second triangle, and their included angles are equal. The included angle is formed by the two sides of the triangle.

3. Two angles of the first triangle equal the corresponding angles of the second triangle, and any pair of corresponding sides are equal.

**Example:**

Triangles *ABC *and *DEF *in the diagrams below are congruent if any one of the following conditions can be met:

1. The three sides are equal

*(sss) = (sss)*

2. Two sides and the included angle are equal

*(sas) = (sas) *

3. Two angles and any one side are equal

*(aas) = (aas) or (asa) = (asa)*

**Example:**

In the equilateral triangle below, line *AD *is perpendicular (forms a right angle) to side *BC*. If the length of *BD *is 5 feet, what is the length of *DC*?

**Medians**

The *medians *of a triangle are the lines drawn from
each vertex to the midpoint of its opposite side. The medians of a triangle
cross at a point that divides each median into two parts:

- One part of one-third the length of the median.
- The other part of two-thirds the length.

**Angle bisectors**

The *angle
bisectors *of a triangle are the lines that divide each angle of the
triangle into two equal parts. These lines meet in a point that is the center
of a circle inscribed in the triangle.

**Altitudes**

The *altitudes
*of the triangle are lines drawn from the vertices perpendicular to the opposite
sides. The lengths of these lines are useful in calculating the area of the
triangle, since the area of the triangle is 1/2(base)(height), and the height
is identical to the altitude.

**Perpendicular bisectors**

The *perpendicular bisectors *of the triangle are
the lines that bisect and are perpendicular to each of the three sides. The
point where these lines meet is the center of the circumscribed circle.

**The sum of any two sides of a triangle
is greater than the third side.
Example: **

If the three sides of a triangle are 4, 2, and *x*, then what is known about the

value of *x*?