Geometry Ch 7 - Similarity

Question 1

Ratio

Answer 1

Comparison of two quantities. You can write the ration of a to b or a : b as the quotent a/b when b ≠ 0

Question 2

Proportion

Answer 2

A statement that two ratios are equal.

Question 3

Extended Proportion

Answer 3

When three or more ratios are equal.

Question 4

Properties of Proportions

Answer 4

Question 5

Cross-Product Property

Answer 5

The product of the extremes is equal to the product of the means.

Question 6

Scale Drawing

Answer 6

A drawing that shows a real object with accurate sizes reduced or enlarged by a certain amount (called the scale). The scale is shown as the length in the drawing, then a colon (“:”), then the matching length on the real thing.

eg. 1 in = 10 ft

Question 7

Similar Polygons

Answer 7

Have corresponding angles that are congruent and corresponding sides that are proportional.

Question 8

Similarity Ratio

Answer 8

The ratio of the lengths of corresponding sides.

Question 9

Golden Rectangle

Answer 9

A rectangle that can be divided into a square and a rectangle that is similar to the original rectangle.

Question 10

Golden Ratio

Answer 10

A special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi ( Φ, φ ), after the 21st letter of the Greek alphabet. … Phi is usually rounded off to 1.618.

Question 11

Angle-Angle Similarity (AA ∼) Postulate

Answer 11

If two angles of one triangle are congruent tot two angles of another triangle, then the triangles are similar.

Question 12

Side-Angle-Side Similarity (SAS ∼) Theorem

Answer 12

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 triangles are similar.

Question 13

Side-Side-Side Similarity (SSS ∼) Theorem

Answer 13

If the corresponding sides of two triangles are proportional, then the triangles are similar.

Question 14

Indirect Measurement

Answer 14

Using similar triangles and measurements to find distances that are difficult to measure directly.

Question 15

The altitude to the hypotenuse of a right triangle…

Answer 15

… divides the triangle into two triangles that are similar to the original triangle and to each other.

Question 16

Geometric Mean

Answer 16

The central number in a geometric progression (e.g., 9 in 3, 9, 27 ), also calculable as the n th root of a product of n numbers. For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that a/x = x/b. This means that x = √ab.

Question 17

The length of the altitude to the hypotenuse of a right triangle…

Answer 17

…is the mean of the lengths of the segments of the hypotenuse.

Question 18

The altitude to the hypotenuse of a right triangle separates the hypotenuse so tha…

Answer 18

… the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.

Question 19

Side-Splitter Theorem

Answer 19

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

Question 20

Corollary to Side-Splitter Theorem

Answer 20

If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

Question 21

Triangle-Angle-Bisector Theorem

Answer 21

If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.