Math notes chapter 10
Angles
An acute angle has a measure less than 90 degrees.
An obtuse angle has a measure more than 90 degrees.
A right angle has a measure exactly 90 degrees.
A straight angle has a measure exactly 180 degrees.
Two angles are complementary if the sum of their measures is 90 degrees.
Two angles are supplementary if the sum of their measures is 180 degrees.
Two angles that share a common side and vertex and do not overlap are called adjacent angles.
When two lines meet at a point, called intersecting lines, the angles opposite each other are called vertical angles.
Vertical angles are congruent angles; which means they have the same measure.
Two lines in the same plane that do not intersect are called parallel lines.
Perpendicular lines intersect to form four right angles.
Angles that occupy corresponding positions when a line intersects two other lines are called corresponding angles.
Triangles
The sum of the angles in a triangle = 180 degrees.
An acute triangle has 3 acute angles.
An obtuse triangle has 1 obtuse angle.
A right triangle has 1 right angle.
An equilateral triangle has 3 congruent sides.
An isosceles triangle has at least 2 congruent sides.
A scalene triangle has no congruent sides.
Polygons
A quadrilateral is a figure with four sides.
Special quadrilaterals:
A trapezoid has exactly 1 pair of parallel sides.
A parallelogram has 2 pairs of parallel sides.
A rectangle has 4 right angles.
A rhombus has 4 equal sides.
A square has 4 right angles AND 4 equal sides.
A pentagon has 5 sides, a hexagon has 6 sides, a heptagon has 7 sides, an octagon has 8 sides.
A diagonal connects two non-adjacent vertices of a polygon.
Similar & Congruent figures
Similar figures have the same shape, but not necessarily same size.
Congruent figures have the same shape and same size.
Transformations
A transformation is a movement of a figure on a plane.
A translation (slide) is when a figure is moved the same distance in the same direction.
A reflection (flip) is when a figure is reflected over a line of reflection creating a mirror image.
A rotation (turn) is when a figure is rotated about a fixed point called the center or rotation. The angle of rotation is the angle formed by rays drawn from the center to corresponding points.
A line of symmetry is a line through a figure that divides the figure into two mirror images of each other.
A figure has rotational symmetry if a turn of 180 degrees or less produces an image that fits exactly on the original.
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