The lesson title
Points and Straight Lines basics
Angles basics
Vertical angles
Parallel lines
Sum of the interior angles of a triangle
Congruence tests for triangles
Problems on congruence tests for triangles
Problems on congruence tests for triangles-2
The lesson title
How to draw a congruent segment and
a congruent angle using a compass and a ruler
How to draw a parallel line passing through
a given point using a compass and a ruler
Isosceles triangles
An altitude, a median and an angle bisector
in the isosceles triangle
Properties of the sides of parallelograms
The line segment joining the midpoints
of two sides of a triangle
The lesson title
Altitudes in an isosceles triangle
Medians in an isosceles triangle
Angles and sides inequality theorems
for triangles
Angle bisectors in an isosceles triangle
The lesson title
A perpendicular bisector of a segment
An angle bisector properties
How to bisect a segment using a compass
and a ruler
How to bisect an angle using a compass
and a ruler
Perpendicular bisectors of a triangle sides
are concurrent
Angle bisectors of a triangle are concurrent
Altitudes of a triangle are concurrent
Properties of diagonals of a parallelogram
Medians of a triangle are concurrent
The lesson title
Median drawn to the hypotenuse
of a right triangle
The Pythagorean Theorem
More proofs of the Pythagorean Theorem
Law of Sines
Law of sines - the Geometric Proof
Solve triangles using Law of Sines
The lesson title
Proof of the Law of Cosines revisited
Solve triangles using Law of Cosines
On what segments the angle bisector
divides the side of a triangle
The length of a median of a triangle
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The property
The length of any side of a triangle does not exceed
the sum of lengths of the other two sides.
Angles - what is this? Comparing angles. Measuring angles.
Adding angles. Types of angles. Supplementary angles.
Complementary angles. Vertical angles - definitions and examples.
Vertical angles are congruent.
Proof of the theorem and examples.
Angles formed by two straight lines and a transverse line.
Postulates on parallel lines.
The sum of the interior angles of a triangle is equal to 180°.
Three postulates are presented for congruency of triangles
(SAS, ASA and SSS) with the detailed discussion.
Problems on congruence tests for triangles are presented.
If two sides in one triangle are congruent to the two sides in
another triangle and the median drawn to one of them in one
triangle is congruent to the median drawn to the congruent
side in the second triangle, then the triangles are congruent.
The property
The first lesson on construction problems. It explains what
the construction problems are and how to draw a congruent
segment and a congruent angle using a compass and a ruler.
This lesson explains how to construct a parallel line
passing through a given point using a compass and a ruler.
If a triangle has two congruent sides, then
the angles opposite to these sides are congruent.
(In an isosceles triangle the angles at the base are congruent).
If a triangle has two congruent angles, then
the sides opposite to these angles are congruent.
(If a triangle has two congruent angles it is isosceles).
In an isosceles triangle the altitude drawn to the base
coincides with the median and the angle bisector.
If in a quadrilateral the opposite sides are parallel in pairs,
then the opposite sides are of equal length in pairs.
If in a quadrilateral two opposite sides are parallel and of
equal length, then two other opposite sides are
parallel and of equal length too.
The straight line connecting midpoints of two sides of a
triangle is parallel to the third side and is half of its length.
If a straight line bisects one side of a triangle and is parallel
to its second side, then it bisects the third side of the triangle.
The property
If a triangle is isosceles, then the two altitudes are
of equal length.
If in a triangle the two altitudes are of equal length, then
the triangle is isosceles.
If a triangle is isosceles, then the two medians are
of equal length.
If in a triangle the two medians are of equal length, then
the triangle is isosceles.
In a triangle, the angle opposite to the longer side
is greater than the angle opposite to the shorter side.
In a triangle, the side opposite to the greater angle
is longer than the side opposite to the smaller angle.
If two triangles have two sides correspondingly congruent
in pairs, and the third sides are not equal, then the
greater included angle corresponds to the greater third side.
If two triangles have two sides correspondingly congruent
in pairs, and the third sides are not equal, then the
greater third side corresponds to the greater included angle.
If a triangle is isosceles, then the two angle bisectors
are of equal length.
If in a triangle the two angle bisectors are of equal length,
then the triangle is isosceles.
The property
A point is equidistant from the endpoints of a line segment
if and only if the point lies on the perpendicular
drawn through the midpoint of the line segment
A point is equidistant from the sides of an angle
if and only if the point lies on the angle bisector
This lesson is on the construction problems. It explains
how to bisect a segment using a compass and a ruler
and how to construct a perpendicular to the given segment.
This lesson is on the construction problems. It explains
how to bisect an angle using a compass and a ruler.
Perpendicular bisectors of a triangle sides
are concurrent
Angle bisectors of a triangle are concurrent
Altitudes of a triangle are concurrent
In a parallelogram, diagonals bisect each other.
If in a quadrilateral the diagonals bisect each other,
then the quadrilateral is a parallelogram.
Medians of a triangle are concurrent
The property
In a right triangle, the median drawn to the hypotenuse,
has the measure half the hypotenuse.
If in a triangle the median has the measure half the length of
the side it is drawn to, then the triangle is a right triangle.
In a right triangle, the median drawn to the hypotenuse
divides the triangle in two isosceles triangles.
The Pythagorean Theorem. The geometric proof is presented
close to that by Euclid in his books "Elements".
Two more proofs of the Pythagorean Theorem are presented.
First one is based on the layout consideration.
Second one uses similar triangles.
Law of Sines is proved. The Trigonometric proof.
Examples are presented showing how to apply the Law
of Sines to solve triangles.
Law of Sines - more Geometric proof.
Examples on solving triangles with the use the Law of Sines.
All possible cases are considered you can meet when solving
triangles with the use the Law of Sines.
The property
Proof of the Law of Cosines
Examples on solving triangles with the use the Law of Cosines.
All possible cases are considered you can meet when solving
triangles with the use the Law of Cosines.
In a triangle, an angle bisector divides the opposite side
in two segments proportional to the ratio of the length
of the two other sides of the triangle.
The formula is derived to calculate the length of the median
via the lengths of the three sides of the triangle.
Examples are presented showing how to use this formula.
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Under the topic
Points and Straight Lines basics
Angles, complementary,
supplementary angles
Angles, complementary,
supplementary angles
Angles, complementary,
supplementary angles
Triangles
Triangles
Triangles
Geometry
Under the topic
Triangles
Triangles
Triangles
Triangles
Triangles
Triangles
Under the topic
Geometry
Geometry
Triangles
Geometry
Under the topic
Triangles
Triangles
Triangles
Triangles
Triangles
Triangles
Triangles
Geometry
Triangles
Under the topic
Geometry
Pythagorean theorem
Pythagorean theorem
Triangles
Triangles
Trigonometry
Under the topic
Trigonometry
Trigonometry
Geometry
Geometry
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In the section
Geometry
Geometry
Geometry
Geometry
Geometry
Geometry
Geometry
Word problems
In the section
Geometry
Geometry
Geometry
Geometry
Geometry
Geometry
In the section
Word problems
Word problems
Geometry
Word problems
In the section
Geometry
Geometry
Geometry
Geometry
Geometry
Geometry
Geometry
Word problems
Geometry
In the section
Word problems
Geometry
Geometry
Geometry
Geometry
Algebra-II
In the section
Algebra-II
Algebra-II
Word problems
Word problems
......
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