Geometry

Question 1

Test for congruent triangles

Answer 1

• SSS - 3 equal corresponding sides
• SAS 2 equal corresponding sides and 1 corresponding angle between them
• ASA - 2 equal corresponding angles and 1 equal corresponding side - can be in any order
• RHS - 2 right angled triangles with equal hypotenuse and 1 other corresponding side

Question 2

Scale Factor

Answer 2

image length/original length

Question 3

Tests for similar triangles

Answer 3

• AAA - 3 corresponding sides in the same ratio
• SSS - the 3 corresponding sides are proportional to each other
• SAS - 2 sides are proportional to 2 sides
  and the included angle is equal - order matters
• Right Angled Hypotenuse Side (RHS) - the hypotenuse and another corresponding side are proportional

Question 4

Chord theorem 1

Answer 4

Chords of an equal length suptend equal angles at the centre of the circle

If AB = CD then ∠AOB = ⦣COD

Question 4

Chord theorem 2

Answer 4

Chords of equal length are of equal distance from the circle

If AB = CD then OE = OF

Question 5

Chord theorem 4

Answer 5

The perpendicular bisectors of every chord of a circle intersec at the centre of the circle

Question 5

Chord theorem 3

Answer 5

The perpendicular from the centre of the circle to the chord bisects the chord and the angle at the centre subtend the chord

If OM ⟂ AB then AM = BM and ∠AOM = ∠BOM

Question 5

Circle theorem 1

Answer 5

The angle at the centre of the circle is twice the angle at a point on the circle subtended by the same arc

Question 6

Circle theorem 2

Answer 6

The angle in a semicircle is 90°

Question 7

Eulers formula

Answer 7

v+f-e=2
v = vertices
f = faces
e = edges