Download Three Dimensional Shapes: Cones (Concepts) by Luana K Mitten PDF
By Luana K Mitten
Introduces cones by means of matching textual content and photograph heavily, and likewise makes use of repetition and easy sentence constitution. additionally on hand in Spanish. comprises full-color images.
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Additional resources for Three Dimensional Shapes: Cones (Concepts)
Sample text
Three parallel lines dravm through the vertices of a triangle ABC meet the respectively opposite sides in the points X, Y, Z. Show that: area XYZ:area ABC= 2:1. 31. If the distance between two points is equal to the sum (or the difference) of the tangents from these points to a given circle, show that the line joining the two points is tangent to the circle. 32. Two parallel lines AE, BD through the vertices A, B of the triangle ABC meet a line through the vertex C in the points E, D. If the parallel through E to BC meets AB in F; show that DF is parallel to AC.
L 14. Construct a right triangle given the altitude to the hypotenuse and the distance of the vertex of the right angle from the trace on a leg of the internal bisector of the opposite acute angle. 15. Construct a rectangle so that one of its vertices shall coincide with a vertex of a· given triangle and the remaining three vertices shall lie on the three circles having for diameters the sides of the triangle. 16. Construct a triangle given a median and the circumradii of the two triangles into which this median divides the required triangle.
He - ~' B, C. 2. h. - hb, b, c. 3. h. - hb, b - c, B - C. 4. - hb, A, b +c. SUPPLEMENTARY EXERCISES 1. Through a given point to draw a circle tangent to two given parallel lines. 2. Through a given point to draw a line passing through the inaccessible point of intersection of two given lines. 3. Draw a line of given direction meeting the sides AB, AC of a given triangle ABC in the points B', C' such that BB' = CC'. 4. Through a given point to draw a line so that the sum (or the difference) of its distances from two given points shall be equal to a given length.