If in a triangle the median has the measure half the length of In a right triangle, the median drawn to the hypotenuse, Then the quadrilateral is a parallelogram. If in a quadrilateral the diagonals bisect each other, In a parallelogram, diagonals bisect each other.
How to bisect an angle using a compass and a ruler. How to bisect a segment using a compass and a rulerĪnd how to construct a perpendicular to the given segment. This lesson is on the construction problems. If and only if the point lies on the angle bisector If and only if the point lies on the perpendicularĭrawn through the midpoint of the line segmentĪ point is equidistant from the sides of an angle If in a triangle the two angle bisectors are of equal length,Ī point is equidistant from the endpoints of a line segment If a triangle is isosceles, then the two angle bisectors Greater third side corresponds to the greater included angle. Greater included angle corresponds to the greater third side. In pairs, and the third sides are not equal, then the If two triangles have two sides correspondingly congruent Is longer than the side opposite to the smaller angle. In a triangle, the side opposite to the greater angle Is greater than the angle opposite to the shorter side.
In a triangle, the angle opposite to the longer side If in a triangle the two medians are of equal length, then If a triangle is isosceles, then the two medians are If in a triangle the two altitudes are of equal length, then If a triangle is isosceles, then the two altitudes are To its second side, then it bisects the third side of the triangle. If a straight line bisects one side of a triangle and is parallel Triangle is parallel to the third side and is half of its length. The straight line connecting midpoints of two sides of a If in a quadrilateral two opposite sides are parallel and ofĮqual length, then two other opposite sides are Then the opposite sides are of equal length in pairs. If in a quadrilateral the opposite sides are parallel in pairs, In an isosceles triangle the altitude drawn to the baseĬoincides with the median and the angle bisector. ( If a triangle has two congruent angles it is isosceles). The sides opposite to these angles are congruent. If a triangle has two congruent angles, then ( In an isosceles triangle the angles at the base are congruent). The angles opposite to these sides are congruent. If a triangle has two congruent sides, then Using a compass and a ruler for three basic cases:ġ) the triangle is given by one side and the two adjacent interior angles Ģ) the triangle is given by two sides and the included angle ģ) the triangle is given by its three sides. This lesson explains how to construct a triangle Passing through a given point using a compass and a ruler. This lesson explains how to construct a parallel line Segment and a congruent angle using a compass and a ruler. The construction problems are and how to draw a congruent The first lesson on construction problems. Side in the second triangle, then the triangles are congruent. Triangle is congruent to the median drawn to the congruent If two sides in one triangle are congruent to the two sides inĪnother triangle and the median drawn to one of them in one Problems on congruence tests for triangles are presented. ( SAS, ASA and SSS) with the detailed discussion. Three postulates are presented for congruency of triangles The sum of the interior angles of a triangle is equal to 180°. Vertical angles - definitions and examples.Īngles formed by two straight lines and a transverse line. Supplementary angles.Ĭomplementary angles. The sum of lengths of the other two sides.Īngles - what is this? Comparing angles. The length of any side of a triangle does not exceed Properties of diagonals of a parallelogram Perpendicular bisectors of a triangle sidesĪngle bisectors of a triangle are concurrent Properties of the sides of parallelograms How to construct a parallel line passing throughĪ given point using a compass and a rulerĪn altitude, a median and an angle bisector
Problems on congruence tests for triangles-2Ī congruent angle using a compass and a ruler Problems on congruence tests for triangles At the end of the list there are links to the lessons on word problems related to triangles. The list consolidates the relevant lessons that are located under different topics and even in the different sections Preceding ones only and does not refer to that follow. The lessons are listed in the logical order, which means that every given lesson refers to the The properties are presented with the links to the corresponding lessons.
The file contains short annotations to the lessons and the major properties of triangles. For your convenience, this file consolidates my lessons on triangles in this site.