Synthetic Geometry

Question 1

a statement accepted without proof, as a basis for argument

Answer 1

axiom

Question 2

a statement deduced from the axioms by logical argument

Answer 2

theorem

Question 3

a statement that follows directly from a theorem

Answer 3

corollary

Question 4

a theorem or corollary in reverse

Answer 4

a converse of a theorem or corollary

Question 5

a series of statements each following logically from the preceding one, starting at an axiom or previously proven theorem and ending with the statement to be proven

Answer 5

proof

Question 6

=>

Answer 6

implies

Question 7

<=>

Answer 7

is equivalent to

Question 8

form of proof that establishes the truth of a statement by proving that the statement being false leads to a contradiction. since a statement must be either true or false, showing its falsity to be impossible proves that the statement must be true

Answer 8

proof by contradiction

Question 9

two points axiom

Answer 9

there is exactly one line through any two given points

Question 10

number of degrees in an angle is always between..

Answer 10

0º and 360º

Question 11

ordinary angle

Answer 11

less than 180º

Question 12

straight angle

Answer 12

180º

Question 13

how many rays from point A at dº

Answer 13

2; clockwise and anticlockwise

Question 14

if an angle is cut and two, the sum of the two is

Answer 14

the same as the original angle

Question 15

3 combinations of congruent triangles

Answer 15

SAS
ASA
SSS

Question 16

explain SAS

Answer 16

2 sides and angles in between

Question 17

explain ASA

Answer 17

2 angles and any side

Question 18

AAA

Answer 18

~ similar triangle

Question 19

theorem; vertically opposite angles

Answer 19

are equal

Question 20

theorem; isosceles triangles (2)

Answer 20

1. the angles opposite the equal sides are equal

2. conversely, if 2 angles are equal then the triangle is isosceles

Question 21

theorem; alternate angles

Answer 21

2 lines are parallel if and only if, alternate angles are equal

Question 22

theorem; sum of angles in triangle

Answer 22

180º

Question 23

theorem; corresponding angles

Answer 23

2 lines are parallel if and only if, for any transversal , corresponding angles are equal

Question 24

theorem; exterior angle

Answer 24

each exterior angle of a triangle is equal to the sum of the interior opposite angles

Question 25

theorem; greater side

Answer 25

the angle opposite the greater of two sides is greater than the angle opposite the lesser

Question 26

greater angle theorem

Answer 26

the side opposite the greater of two angles is greater than the side opposite the lesser angle

Question 27

theorem; triangle inequality

Answer 27

the sum of two sides of a triangle is greater than the third

Question 28

theorem; equals in a parallelogram

Answer 28

in a parallelogram, opposite sides are equal and opposite angles are equal, converses also equal

Question 29

corollary; divides diagonal

Answer 29

a diagonal divides a parallelogram in 2 congruent triangles

Question 30

theorem; bisect parallelogram

Answer 30

the diagonals of a parallelogram bisect each other

Question 31

theorem; transversal cutting parallel lines

Answer 31

if 3 parallel lines cut off equal segments on some transversal line they will cut off equal segments on any other transversal

Question 32

theorem; lines parallel to the base of the triangle

Answer 32

let ABC be a triangle, if a line l is parallel to BC and cuts AB in the ratio m:n, then it also cuts AC in the same ratio

Question 33

theorem; similar triangles have proportional sides

Answer 33

if 2 triangles ABC and A’B’C’ are similar, then their sides are proportional in order:
lABl lBCl lCAl
—— = —— = ——-
lA’B’l lB’C’l lC’A’l

Question 34

theorem; area of parallelogram

Answer 34

base by the height

Question 35

theorem; same arc angles

Answer 35

angle at the centre of a circle standing on a given arc is twice the angle standing on the same arc at the edge of the circle

Question 36

corollary; same arc same angles

Answer 36

all angles at points of the circle, standing on the same arc, are equal

Question 37

corollary, semicircle angle

Answer 37

each angle in a semi circe is a right angle

Question 38

theorem; cyclic quadrilateral

Answer 38

in a cyclic quadrilateral, opposite angles are equal

Question 39

if two angles share a common tangent at one point

Answer 39

then the two centres of the circles are co-linear

Question 40

the perpendicular bisector of a chord

Answer 40

passes through the midpoint