Chap 19 - symmetry, circle geometry

Question 1

define axis of symmetry

Answer 1

where the symmetry line is

Question 2

dimensions for:
lines of symmetry
rotational symmetry
planes of symmetry

Answer 2

lines of symmetry
rotational symmetry - 2D
planes of symmetry - 2D

Question 3

how many lines of symmetry & rotational symmetry is there for a circle

Answer 3

infinite

Question 4

how many lines of symmetry & rotational symmetry is there for a parallelogram

Answer 4

lines of symmetry - 0
rotational symmetry - 2

Question 5

how many lines of symmetry & rotational symmetry is there for a rhombus

Answer 5

lines of symmetry - 2
rotational symmetry - 2

Question 6

note: mark radiuses

Question 7

2 tangents touch a circle from a point:

Answer 7

-angle btw tangent and radius = 90
-tangents are equal
-can be bisected

Question 8

2 triangles with 2 same conners or a quadrilateral that touches the center and the circumferences

Answer 8

-the angle at the center is twice the angle at the other side

Question 9

triangle with a diameter as one of its sides

Answer 9

-triangle is right angled

Question 10

2 triangles that looks like a butterfly. line does not go through center

Answer 10

-angles in the same segment are equal
-similar triangles; same angles with diff lengths.
-lengths of opposite sides are in the same fraction for similarity

Question 11

2 triangles that looks like a drunk butterfly. line does go through center

Answer 11

-angle at the center is twice the angle at the circumference

Question 12

a cyclical quadraliteral

Answer 12

-opposite angles in a cyclical quadrilateral add up to 180

Question 13

alternate segments theorem (AST)

Answer 13

-angle on a side is equal to the angle of a triangle
(look at diagram)
-triangle doesn’t have to go through center
-triangle conners need to touch circumference

Question 14

Proofing statements

Answer 14

1) The center angle is twice the circumference angle on the same arc
2) A diameter subtends a 90 angle at the circumference
3) Angles from the same arc are equal
4) Opposite angles in a cyclic quadrilateral add up to 180
5) The radius perpendicular to the radius at the point of contact forms a 90 degree
6) A tangent is perpendicular to the radius at the point of contact forms a 90 degree
7) Alternate segment: the angle between a tangent & chord equals the angle in the alternate segment