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What sort of angles are the two others? The two others are acute angles.

What sort of angles has the obtuse-angled triangle? One obtuse and two acute angles, &c.


Further development in regard so some essential mathematical figures.

The mother draws quadilateral figures of

four equal sides. A four-sided figure . .

which has all its sides equal, and all its

angles right angles, is called a square.''

Try whether the square I have drawn is correct. She makes three squares of equal, and two of unequal magnitude. How many equal sides has a square? how many right angles?

A four-sided figure, which i —.

has all its angles right an-
gles, but not all its sides
equal, is called an oblong, or parallelogram.

She makes two, three, four oblongs of equal, and as many of unequal size.

I will draw a four-sided figure, which has all its sides equal, but whose angles are not right, but acute and obtuse angles. Such a figure is called a rhomb. She draws a figure which has its opposite sides equal to one another, but which has not all its sides equal, nor its angles right angles. This figure is called a rhomboid. She makes three, four, five rhomboids, of equal and unequal size, which the children describe. Can you show me in any other place besides the table or slate, a square, an oblong, a rhomb, or a rhomboid?

We will draw an irregular four-sided figure: such a figure is called a trapezium.

Mother. Here is a five-sided figure, or pentagon, having all its sides equal, and five obtuse angles. Can you form such a figure, and express, by words, what you have been doing? This figure is called an equal-sided or equilateral pentagon.


Here is a pentagon of two and of three equal sides, having two right, two equal obtuse, and one acute angle.


Here is one having two and two sides equal and one unequal, having five acute angles.

Here is a six-sided figure, or hexagon, having all its sides equal, and therefore called an equilateral hexagon.


Drawing Exercise. Combination of Angles, Triangles, and Polygons.

Mother. Form a combination of parallel lines equally long, running in different directions. Form another of right angles, either combined or separate. Another of acute angles, of equal magnitude. A third of equal and unequal obtuse angles, &c.


Make a combination of equilateral triangles, of equal magnitude: another of isosceles, or such triangles as have only two sides equal. A figure which is composed of right-angled triangles. Another of equal obtuse triangles, &c.


Draw a figure by combining equilateral triangles with right angles: another by right-angled triangles with acute angles, &c.

Compose a figure of equal squares.


Draw figures by a combination V \ of rhombs: j ^ ^

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Form different figures , .

by a combination of ~7 I \

equal lines, drawn in ^—y, difFerent directions. 2

Draw a figure by a combination of equal angles joining each other:

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