October 23

Assignment 4

Triangles and Circles Exercises | Median Exercises | Altitude Exercises
Construction Exercises

Exercises

Triangles and Circles:

1) p. 105, Ex. 7.1, 7.2, 7.3

2) Construct any triangle and its escircles and incircle. Show that the Inscribed and Escribed Area Corollaries are true.

3) Construct a quadrilateral whose four vertices are on a circle. This type of quadrilateral is called a cyclic quadrilateral. Can you find a modification of Heron's theorem for this type of quadrilateral?

4) Does your theorem hold for any quadrilateral?

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Medians and Centroids

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1) pp. 114 -115, Ex. 8.2, 8.8,

2) p. 115, use Sketchpad to show 8.9 and 8.10. Once you have your calculations, can you justify them?

3) Use Sketchpad to find a relationship between:

a) The sum of the squares of the lengths of the medians of a triangle and the sum of the squares of the lengths of the sides of the triangle.

b) The sum of the squares of the segments joining the centroid with the vertices and the sum of the squares of the lengths of the sides of the triangle.

c) Can you justify your conclusions?
 

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Altitudes and Orthocenters

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For problem 9.1, use a triangle such as this one seen on the right with the smaller triangle BCH formed by the orthocenter and two vertices of the original triangle.

1) p. 126, Ex. 9,1

2) If is equilateral, what is the relationship between the incircle and the 9 point-circle?

3) p.127, Ex. 9.7, 9.9

Constructions with Indirect Elements

p. 147, Ex. 11.2, 11.3, 11.4, and 11.6
 

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