# Geomtery...nom nom

## 21 terms

### ratio

is a comparison of two quantities

### proportion

is a statement that two ratios are equal

### extended proportions

when three or more tatios are equal

### Cross-Product property

multiplying borh sides of a/b=c/d by bd results in the first property

### Scale drawing

a drawing of atleast two figures that are similar

### Scale

Compares each length in the drawing to the actual length

### similar

Two polygons are similar is (1) corressponding angles are congruent and (2) corresponding sides are congruent

### similarity ratio

the ratio of the length of corresponding sides

### golden rectangle

is a rectangle that can be divided into a square and a rectangle, that is similar to the orginal rectangle

1.618:1

### Indirect measurament

using similar triangle and measureaments to find distances that are difficult to measure directly

### Angle-Angle Similarity

If two angles of one triangle are congruent to two angles of another triangle then the triangles are similar

### Side Angle Side

If an angle of one triangle is congruent to an angle of a second triangle and the sides including the two angles are proportional then the triangle are similar

### Side Side Side

If the corresponding sides of teo triangle are porportional then the triangels are similar

### Geometric means

proportions in which the means are equal occur frequently in geometry

### Theorem 7-3

the altitude to the hypothenus of a triangle dived the triangle into two triangles that are similar to the orginal triangle and to each other

### Corollart 1 to Thereom 7-3

The lengrh of the altitude to the hypotenuse of a right triangle is teh geometric mean of the length of the segement of the hypotenuse

### Corollary 2 to theorem 7-3

The altitude to the hypotenuse of oa right triangle seperates teh hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenus segement and the length of the hypotenuse

### Side Splitter Theorem

If a line is parallel to one side of a triangle and intersects the other two sides then it divides those sides proporortionally

### Corollary to theorem 7-4

If three parallel lines intersect two transversals then the segment intercepted on the transversals are proportional

### Triangle Angle Bisector thm

If a ray bisects an angle of a triangle then it dived the opposite side into two segments that are porportional to the other two sides of the triangle