Hachie Chapter 7

Question 1

Properties of Proportions

a/b = c/d is equivalent to

Answer 1

1) ad = bc 2) b/a = d/c

3) a/c = b/d 4) (a+b)/b = (c+d)/d

Question 2

Cross-Product Property

Answer 2

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

Question 3

Side-Angle-Side Similarity (SAS~) Theorem

Answer 3

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 4

Angle-Angle Similarity (AA~) Theorem

Answer 4

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

Question 5

Side-Side-Side Similarity (SSS~) Theorem

Answer 5

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

Question 6

The altitude to the hypotenuse of a right triangle

Answer 6

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

Question 7

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

Answer 7

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

Question 8

The altitude to the hypotenuse of a right triangle separates the hypotenuse so that

Answer 8

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 9

Side-Splitter Theorem

Answer 9

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

Question 10

Corollary to the Side-Splitter Theorem

Answer 10

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

Question 11

Triangle-Angle-Bisector Theorem

Answer 11

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.