Plane Geometry

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Page 224 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 182 - If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle...
Page 80 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 26 - The two pairs of angles 3 and 6, 4 and 5, are called alternate interior angles ; and the two pairs of angles if 1 and 8, 2 and 7, are called alternate exterior angles. The four pairs of angles 1 and 5, 2 and 6, 3 and 7, and 4 and 8 are called corresponding angles.
Page 69 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 230 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 184 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.
Page 175 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 192 - If two chords intersect within a circle, the product of the segments of the one is equal to the product of the segments of the other.
Page 242 - Prove that the area of the square on the hypotenuse of a right triangle equals the sum of the areas of the squares on the other two sides.

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