Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to one half the third side."

Line Joining Midpoints on a Triangle

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to…

Illustration to show that when lines from two opposite vertices of a parallelogram to the midpoints of the opposite sides are drawn, they trisect the diagonal.

Parallelogram With Lines From opposite Vertices to Midpoints

Illustration to show that when lines from two opposite vertices of a parallelogram to the midpoints…

Quadrilateral with intersecting diagonals and segment connecting midpoints.

Quadrilateral With Diagonals and Midpoints Joined

Quadrilateral with intersecting diagonals and segment connecting midpoints.

Illustrations to show quadrilaterals with lines joining the midpoints of the sides of any quadrilateral, taken in order.

Quadrilaterals With Lines Joining Midpoints

Illustrations to show quadrilaterals with lines joining the midpoints of the sides of any quadrilateral,…

Illustrations to show trapezoids with lines joining the midpoints of the sides of any quadrilateral, taken in order.

Trapezoids With Lines Joining Midpoints

Illustrations to show trapezoids with lines joining the midpoints of the sides of any quadrilateral,…

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the triangle into four equal triangles.

Midpoints of Triangle Divide Triangle into Four Equal Triangles

Illustration to show that if the lines joining the middle points of the sides of a triangle divide the…

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles triangle are equal.

Perpendiculars Dropped From Midpoint of Base to Legs of Isosceles Triangles

Illustration to show the perpendiculars dropped from the midpoint of the base to the legs of an isosceles…

Illustration of an equilateral triangle inscribed in an equilateral triangle. The smaller triangle is created by joining the midpoints of the sides of the larger triangle. The area of the inscribed triangle is 1/4 the area of the larger triangle.

Equilateral Triangle Inscribed In An Equilateral Triangle

Illustration of an equilateral triangle inscribed in an equilateral triangle. The smaller triangle is…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. 3 smaller equilateral triangles are then constructed in the remaining area by joining the midpoints of the other 3 triangles.

Equilateral Triangles Inscribed In An Equilateral Triangle

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. Thus, there are 4 equilateral triangles inside of the large triangle. Inside each of the 4 smaller equilateral triangles another equilateral triangle is constructed by joining the midpoints of the sides.

Equilateral Triangles Inscribed In Equilateral Triangles

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints of the sides of the larger triangle. Inside the smaller equilateral triangle another inscribed equilateral triangle is constructed by joining the midpoints of the sides.

Equilateral Triangles Inscribed In Equilateral Triangles

Illustration of an equilateral triangle inscribed in an equilateral triangle by joining the midpoints…