ch.8 geometry 1 Flashcards
difference between complementary angles & supplementary angles
complementary - 2 angles that add up to 90* (e.g. 48 and 42)
supplementary - 2 angles that add up to 180* (e.g. 125 and 55)
sum of angles in a triangle?
180 degrees
sum of angles in a circle?
360 degrees
sum of angles in a quadrilateral?
360 degrees
what are similar triangles?
triangles that look alike but are not the same
what are congruent triangles?
triangles that look alike, same size - exactly same shape and size
how do yk if a triangle is congruent?
- sss (3 sides in one triangle = 3 sides in the other)
- sas (2 sides and included angle in one triangle = 2 sides and included angle in other)
- asa (2 angles and side between them are equal in measure in each)
important parts of a right-angled triangle and their definitions
- hypotenuse: longest side, opposite right angle
- opposite: side across from a given angle
- adjacent: side next to a given angle
what is the pythagoras theorem?
in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other 2 sides
what is the theorem of pythagoras in algebra?
a2 = b2 + c2
what is the converse of the pythagoras theorem?
if the square on one side of a triangle is equal to the sum of the squares on the other 2 sides, then the angle opposite the first side is a right angle
line segment
the line segment [AB] starts at A and ends at B
A •———–• B
ray (line)
the line that starts at A and continues on through B is called the ray [AB
A •————-•B———->
collinear (lines)
points that lie on the same line are said to be collinear
A •—————•B———-•C——-
intersect (lines)
the lines l and m intersect at the point p
l \p/ m
/ \
parallel lines
lines that never meet
———>————
———>————
how do u write an angle
put the name of the angle ur talking abt in the middle (e.g.
straight angle
a half a revolution makes a straight angle
straight angle = 180 degrees
acute angle
an angle less than 90 degrees
obtuse angle
an angle between 90 and 180 degrees
reflex angle
an angle between 180 and 360 degrees
vertically opposite angles
if angles are vertically opposite they are equal in measure
angles at a point
angles at a point add up to 360 degrees
corresponding angles (parallel lines)
corresponding angles are equal
- looks for an F shape
alternate angles (parallel lines)
alternate angles are equal
- look for a Z shape
interior angles (parallel angles)
interior angles add up to 180 degrees
equilateral triangle
- 3 equal sides
- 3 equal angles
- each angle = 60 degrees
isosceles triangle
- 2 equal sides
- base angles are equal
right-angled triangle
- has an angle of 90 degrees
