The lengths of PG is 17. To find the length of PT, recognize that PT is an altitude of right triangle SPH. The area of this triangle is 60 square units (how?). The length of SH is 17. The length of the altitude to side SH is 120/17 (how?)

Problem 3

(a) Which of the special line, by definition, go through a vertex?
(b) Is it possible for a median to be perpendicular to the side to which it is drawn?
(c) Is it possible for an altitude to bisect the vertex angle to which it is drawn?

Problem 4

The diagonals of a rhombus are (1) perpendicular and (2) bisect each other (because it is a parallelogram). Therefore, a rhombus consists of four congruent right triangles. Each side of the rhombus must be 20. Should be 15-Stephen M

Problem 5

Problem 6

Problem 7, 8, 9

Watch the pencast below, then try typing in the results into the input line in the applet.

On the applet below, which shows a trapezoid, drag DRAG ME until the midpoints of the diagonals concur.

Problem 12

Problem 13

Problem 14

Problem 15

Page 40

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

What can be said about a quadrilateral, if it is known that every one of its adjacent angle
pairs is supplementary? I think you have proved this.

Problem 7

If there are nine vertices, there are nine sides, and there are nine exterior angles. By the Sentry Theorem, the exterior angle add up to 360 degrees, so each exterior angle is 40 degrees, so each interior angle is 140 degrees.

Problem 8

Is it possible for the sides of a triangle to be 23, 19, and 44? NO. According to the triangle inequality theorem, the two smaller side must sum to MORE than the largest side. In this case, 23+19=42.

## Table of Contents

## Page 39

## Problem 1 and 2

The lengths of PG is 17. To find the length of PT, recognize that PT is an altitude of right triangle SPH. The area of this triangle is 60 square units (how?). The length of SH is 17. The length of the altitude to side SH is 120/17 (how?)

## Problem 3

(a) Which of the special line, by definition, go through a vertex?

(b) Is it possible for a median to be perpendicular to the side to which it is drawn?

(c) Is it possible for an altitude to bisect the vertex angle to which it is drawn?

## Problem 4

The diagonals of a rhombus are (1) perpendicular and (2) bisect each other (because it is a parallelogram). Therefore, a rhombus consists of four congruent right triangles. Each side of the rhombus must be 20. Should be 15-Stephen M

## Problem 5

## Problem 6

## Problem 7, 8, 9

Watch the pencast below, then try typing in the results into the input line in the applet.

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## Problem 10

Play with the applet, which illustrates quadrilaterals with congruent diagonals.

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## Problem 11

On the applet below, which shows a trapezoid, drag DRAG ME until the midpoints of the diagonals concur.

## Problem 12

## Problem 13

## Problem 14

## Problem 15

## Page 40

## Problem 1

## Problem 2

## Problem 3

## Problem 4

## Problem 5

## Problem 6

What can be said about a quadrilateral, if it is known that every one of its adjacent angle

pairs is supplementary? I think you have proved this.

## Problem 7

If there are nine vertices, there are nine sides, and there are nine exterior angles. By the Sentry Theorem, the exterior angle add up to 360 degrees, so each exterior angle is 40 degrees, so each interior angle is 140 degrees.

## Problem 8

Is it possible for the sides of a triangle to be 23, 19, and 44? NO. According to the triangle inequality theorem, the two smaller side must sum to MORE than the largest side. In this case, 23+19=42.

## Problem 9

## Problem 10

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## Problem 11

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## Problem 12

## Problem 13

## Problem 14

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## Problem 15

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