Geometry

Question 1

Congruent triangle conditions

Answer 1

SSS / SAS / ASA / RHS

Question 2

Axiom

Answer 2

statement accepted without proof

Question 3

Theorem

Answer 3

statement that can be proven using axioms and logical argument

Question 4

Corollary

Answer 4

statement which follows logically from the result of a theorem

Question 5

Converse

Answer 5

reverse statement of theorem
[if a triangle is isoceles then its base angles are equal in measure
= if two angles in a triangle are equal then it is isoceles] - converse is true
Converse may be true or false depending on theorem

Question 6

Theorem 1

Answer 6

Vertically opposite angles are equal in measure

Question 7

Theorem 2

Answer 7

In an isosceles triangle the angles opposite the equal sides are equal

Question 8

Theorem 3

Answer 8

If a traversal makes equal angles on two lines then the lines are parallel
[Converse: if two lines are parallel then a traversal will make equal angles on them]

Question 9

Theorem 4

Answer 9

Angles in a triangle add up to 180

Question 10

Theorem 5

Answer 10

Two lines are parallel only if for any transversal the corresponding angles are angles

Question 11

Theorem 6

Answer 11

Each exterior angle of a triangle is equal to the sum of the interior opposite angles
|C exterior| = |A| + |B|

Question 12

Theorem 7

Answer 12

In a triangle the greater the side length, the greater the opposite angle

Question 13

Theorem 8

Answer 13

Two sides of a triangle added together are always greater than the third

Question 14

Theorem 9

Answer 14

In a parallelogram, opposite sides are equal and opposite angles are equal
Corollary[A diagonal dives a parallelogram into two congruent triangles]

Question 15

Theorem 10

Answer 15

Diagonals of a parallelogram bisect each other (cut each other perfectly in half)

Question 16

Theorem 11

Answer 16

If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal

Question 17

Theorem 12

Answer 17

A line drawn parallel to one side of a triangle divides the other sides in the same ratio

Question 18

Theorem 13

Answer 18

If two triangles are similar, then their sides are proportional

Question 19

Theorem 14

Answer 19

(Pythagoras Theorem) In a right angles triangle, hypotenuse squared is equal to the sum of the squares of the other two sides

Question 20

Theorem 15

Answer 20

(Converse of Pythagoras) If the square of one side of a triangle is the sum of the squares of the other two, then the angle opposite the first side is a right angle

Question 21

Theorem 16

Answer 21

In a triangle, base X height does not depend on the choice of base. i.e. you can use any of the 3 sides as the base with their respective height

Question 22

Theorem 17

Answer 22

Diagonal of a parallelogram bisects the area

Question 23

Theorem 18

Answer 23

Area of a parallelogram is base X height

Question 24

Theorem 19

Answer 24

Angle at the centre of a circle is twice the angle at the circumeference when both angles are standing on the same arc
Creates a number of corollaries

Question 25

Corollary 1

Answer 25

All angles at points of a circumference, standing on the same arc, are equal in measure

Question 26

Corollary 2

Answer 26

Angles in a semicircle are right angles / Angles standing on a diameter of a circle are right angles

Question 27

Corollary 3

Answer 27

If the angle standing on a chord of a circle is a a right angle then the chord is a diameter

Question 28

Corollary 4

Answer 28

If all 4 corners of a quadrilateral are on the circumference of a circle, then opposite angles in the quadrilateral add up to 180

Question 29

Theorem 20

Answer 29

A tangent is perpendicular to the radius that goes to the point of contact If a line is perpendicular to the radius at a point on a circumference, then that line is a tangent

Question 30

Theorem 21

Answer 30

On a circle chord, the perpendicular from the centre to the chord bisects it. Converse: Perpendicular bisector of a chord passes through the centre Corollary: If two circles touch/intersect at only one point, then the two centres and the point of contact form a straight line

Question 31

RHS congruentcy

Answer 31

If both triangles have a right angle, an equal hypotenuse and one other equal side

Question 32

mediator

Answer 32

perpendicular bisector of a side of a triangle

Question 33

Circumcentre

Answer 33

Where the mediators intersect

Question 34

altitude

Answer 34

perpendicular line from line to opposite corner

Question 35

Orthocentre

Answer 35

Where altitudes intersect

Question 36

Incentre

Answer 36

Where bisectors of angles intersect

Question 37

median

Answer 37

line from midpoint of line to opposite corner

Question 38

Centroid

Answer 38

where medians intersect