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### Theorm 8-1

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

### Corollary 1:

When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the segments of the hypotenuse.

### Corollary 2:

When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

### Pythagorean Theorem

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

### Theorem 8-3

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

### Theorem 8-4

If the square of the longest side of a triangle is less than the sum of the squares of the other sides, then the triangle is an acute triangle.

### Theorem 8-5

If the square of the longest side of a triangle is greater than the sum of the squares of the other two sides, then the triangle is an obtuse triangle.

### Theorem 8-7 (30-60-90)

In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg.

### Theorem 9-1

If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

### Theorem 9-2

If a line in the plane if a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle.

### Theorem 9-3

In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.

### Theorem 9-4

In the same circle or in congruent circles; A) congruent arcs have congruent, B) congruent chords have congruent arcs.

### Theorem 9-6

In the same circle or in congruent circles; A) chords equally distant from the center (centers) are congruent, B) congruent chords are equally distant from the center (centers).

### Corollary 3:

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

### 9-8

The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

### 9-9

the measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.

### 9-10

The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the intercepted arcs.

### 9-11

When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord.

### 9-12

When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segment and its external segment.

### 9-13

When a secant segment and a tangent segment are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment.

### 11-5

The area of a trapezoid equals half the product of the height and the apothem and the perimeter. (A=1/2ap)

### 11-7

If the scale factor of tow similar figures is a:b, then; 1) the ratio of the perimeters is a:b, 2) the ratio of the areas is a2:b2.

### 12-1

The lateral area of a right prism equals the perimeter of a base times the height of the prism.

### 12-3

The lateral area of a regular pyramid equals half the perimeter of the base times the slant height.

### 12-5

The lateral area of a cylinder equals the circumference of a base times the height of the cylinder.

### 12-11

The scale factor of two similar solids is a:b, then 1)the ratio of corresponding perimeters is a:b 2) the ratio of the base areas, of the lateral areas, and of the total areas is a2:b2 3) the ratio of the volumes is a3:b3

### 13-6 (Standard Form)

The graph of any equation that can be written in the form Ax+By=C, with a and b not both zero, is a line.