Hello everyone, I’m also a math learner. For me, the properties of the triangle are an important part of the curriculum. However, some people still find it difficult to synthesize this knowledge array. Let’s come to learn easier with “RESUMIND”. In addition, Please scroll down to the yellow fill for instructions!

## 1. The properties of the triangle with RESUMIND: Basic properties of the triangle.

• The sum of 3 angles in a triangle equals 180 degrees
• The measure of the outer angle is the sum of the two inner angles not adjacent to it.

## 2. The properties of the triangle with RESUMIND: The two triangles are equal.

• The two triangles are equal when these two triangles have their respective edges and their respective angles are equal.
• The two triangles are equal in the case of “edge-angle-edge” when their respective edges are equal and the angle between the two edges is equal.
• The two triangles are equal in the case of “angle-edge-angle” when their two respective angles are equal & the edge between the two corners is equal.
• The two triangles are equal in the case of “edge-edge-edge” when their 3 respective edges are equal.
• The two right-angled triangles are equal in the following cases: 2 right-angled edges, a right-angled edge & sharp angles adjacent to it, hypotenuse & sharp angle, hypotenuse & a right-angled edge.

## 3. The properties of the triangle with RESUMIND: equiangular triangle, isosceles triangle

• Isosceles triangles have 2 equal edges and 2 equal angles.
• Equiangular triangles have 3 equal edges and 3 equal angles & equal to 60 degrees.
• An equiangular triangle is an isosceles triangle with an angle equal to 60 degrees.

## 4.The properties of the triangle with RESUMIND: Inequality in a triangle

In a triangle: the sum of any 2 edges is always greater than the other, the difference of any 2 edges is always less than the other.

## 5. Special lines in the triangle

• The median line is the straight line connecting the vertex with the midpoint of the opposite edge.
• The altitude is the straight line going through the vertex and perpendicular to the opposite edge.
• The bisector is the straight line that divides this angle into two angles that have equal magnitude.
• The centerline of a straight line is a straight line perpendicular to this straight line at its midpoint.
• 3 median lines, 3 altitudes, 3 bisectors converge at one point.
• The midline of a triangle is the straight line connecting the midpoint of the two opposite edges.

## 6. Thales’s theorem

• Firstly, If a straight line is parallel to one edge of a triangle, it will divide the other two edges into the respective proportional segments.
• Secondly, If a straight line divides the two edges of a triangle into the respective proportional segments, it will be parallel to the other edge.
• Thirdly, If a straight line divides the two edges of a triangle into the respective proportional segments and is parallel to the other edge, it will form a new triangle with 3 edges respectively proportional to the 3 edges of the original triangle.

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