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equal and one unequal. Four, of which two are equal and two unequal. Five, of which three are equal and two unequal, &c.

In the same manner, one pair of equal parallel lines, and another pair of equal parallel lines, but the pairs unequal betwixt themselves.

Try to describe all that you see on the slate.

SECTION XIII.

Lines in any direction, in contact or separate, of equal and unequal lengths.

Mother. Draws two, three, four, five lines of equal length in contact with each other.

She draws the same number in contact with each other, but of unequal length. Two, three, four, &c. separate perpendicular lines of equal length: as many of the same description, but of unequal length.

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SECTION XIV.

Denomination of Angles.

The mother draws these angles, saying; the the first of these angles is called an acute, the second a right, the third an obtuse angle.

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In order to show him, in an easy manner, the difference between them, she may draw acute angles of different magnitude, always increasing until she comes to the right angle, and, by increasing the right, proceed to the obtuse angle, which may still be increased till it becomes a straight line.

Mother. I will make one, two, and four right angles with two lines.

Can three right angles be formed with two lines? Four acute angles—four obtuse, &c. Describe what I have drawn. She makes acute angles of equal magnitude: obtuse, of equal magnitude: acute and obtuse angles of unequal magnitude. Can you make right angles of unequal magnitude?

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Should the child imagine that this can be done, the mother, by drawing right angles in various directions, will lead him to discover that right angles cannot be unequal, but are always of equal magnitude.

I will draw lines meeting in one point, and you shall count the angles so formed, mentioning at the same time what sort of angles they are.

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SECTION XV.

Triangle.Length of the Sides.

Mother. Makes a triangle of three equal lines. The lines which form a triangle are called the sides of the triangle. A triangle

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which has three equal sides is called an equilateral triangle. Do you think I can make a triangle, two sides of which are equal and one unequal. Such a triangle is called an isosceles triangle.

I will make a triangle which has three unequal sides. This is called a scalene triangle.

She draws two equilateral triangles. Three isosceles triangles. Four scalene triangles. Draw three equilateral, two isosceles, and one scalene triangle. We will measure whether my equilateral triangle really has three equal sides.

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SECTION XVI.

Form of the Triangle.

We will try whether we can produce a triangle -with a right angle. Such a triangle is called a rightangled triangle.

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Now one with an obtuse angle. This called an obtuseangled triangle.

A triangle with three acute angles is called an acute-angled triangle.

Now three right-angled, two obtuse-angled, and four acute-angled triangles.

SECTION XVII.

Position of Triangles.

The mother makes some triangles which join each other; some which are separate, &c.

SECTION XVIII.

Repetition of some of the foregoing Exercises.

Mother. How many right angles has a right-angled triangle?

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