theorems page 3

Question 1

isosceles trapezoid base angles converse

Answer 1

if a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid

Question 2

isosceles trapezoid diagonals theorem

Answer 2

A trapezoid is isosceles if and only if it’s diagonals are congruent

Question 3

trapezoid midsegment theorem

Answer 3

The midsegment of a trapezoid is parallel to each base and it’s lengths is one half the sum of the lengths of the bases

Question 4

kite diagonals theorem

Answer 4

if a quadrilateral is a kite then it’s diagonals are perpendicular

Question 5

kite opposite angles theorem

Answer 5

if a quadrilateral is a kite then exactly one pair of opposite angles are congruent

Question 6

perimeters of similar polygons

Answer 6

if two polygons are similar then the ratio of their perimeters is equal to the ratios of their corresponding side lengths

Question 7

areas of similar polygons

Answer 7

if two polygons are similar then the ratio of their areas is equal to the squares of the ratios of their corresponding side lengths

Question 8

angle angle similarity theorem

Answer 8

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

Question 9

Side side side similarity theorem

Answer 9

if the corresponding side lengths of two triangles are proportional then the triangles are similar

Question 10

Side angle side similarity

Answer 10

if an angle of one triangle is congruent to an angle of a second triangle and the links of the sides including these angles are proportional then the triangles are similar

Question 11

triangle proportionality theorem

Answer 11

if a line is parallel to one side of a triangle intersect the other two sides then it divides the two sides proportionally

Question 12

Converse of the triangle proportionality theorem

Answer 12

if a line divides two sides of a triangle proportionally then it is parallel to the third side

Question 13

three parallel lines theorem

Answer 13

if three pair well lines intersect to transversal’s then they divide a transversal’s proportionally

Question 14

triangle angle by sector theorem

Answer 14

if a ray by six and angle of a triangle then it divides the opposite sides into segments who’s lengths are proportional to the lengths of other two sides

Question 15

pythagorean theorem

Answer 15

in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs

Question 16

Converse of the Pythagorean theorem

Answer 16

if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides in the triangle is a right triangle

Question 17

45-45-90 triangle theorem

Answer 17

in a 45-45-90 triangle, the ratio is 1:1:radical 2

Question 18

30-60-90 triangle theorem

Answer 18

in a 30-60-90 triangle the ratio is 1: radical 3: 2

Question 19

right triangle similarity theorem

Answer 19

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

Question 20

geometric mean (altitude)

Answer 20

the altitude is the geometric mean between the 2 segments of the hypotenuse

Question 21

geometric mean (leg)

Answer 21

each leg is the geometric mean between the hypotenuse and the segments of the hypotenuse that is adjacent to the leg.

Question 22

law of sines

Answer 22

sinA =sinB=sinC
___________________
a. b. c