Chapter seven

Question 1

Side Splitter Theorem

Answer 1

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

Question 2

Triangle Midsegment Theorem

Answer 2

if the points of a line segment are the midpoints of two sides of a triangle, then it is parallel to the other side and it is 1/2 the length of the side it is parallel to

Question 3

Corollary to the Side splitter Theorem

Answer 3

if three parallel lines intersect two transversals, the segments on the transversal are proportional

Question 4

Triangle Angle Bisector Theorem

Answer 4

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

Question 5

Geometric Mean formula (only applicable on right triangles)

Answer 5

m = √a * b
(a = other segment that altitude divides, b = the other half)

Question 6

Theorems to prove that triangles are similar

Answer 6

AA~ , SSS~ , SAS~

Question 7

Properties of a right isosceles triangle

Answer 7

Other two angles are 45 degrees
the legs are the same length
leg times √2 is hypotenuse
hypotenuse divided by √2 is leg

Question 8

Properties of half an equilateral triangle

Answer 8

Angles are 30, 60, and 90 degrees
short leg is x
hypotenuse is 2x
short leg times √3 is long leg
long leg divided by √3 is short leg