Polygons chp 8 Flashcards
Describe the exterior angle sum theorem
IF THE POLYGON IS COVEX : The sum of the measures of the exterior angles is 360
What is the interior angle sum theorem
S= 180(n-2)
n is sides of the polygon
S is the sum of measures of its interior angles
How to find the sum of measures of an exterior angles if the polygon is convex?
Divide number of angles by 360
What is a parallelogram?
Quadrilateral with both pairs of opposite sides parallel
List the four statements that are true if the object is a parallelogram
- Opposite sides of a parallelogram are congruent
- Opposite angles of a parallelogram are congruent
- Consecutive angles of a parallelogram are supplementary
- Parallelogram has one right angle that it has four right angles
What are the diagonals of a parallelogram?
They bisect each other inside the parallelogram
List the three statements that are true about the diagonals of a parallelogram
1.Each bisected part is congruent
Ex: AP = PC see lesson 8-2
2. Separates the parallelogram into two congruent triangles
3. Alternate interior angles are formed by the diagonals
What makes a quadrilateral a parallelogram?
- both pairs of opposite sides parallel
- Opposite sides and angles are congruent
- Consecutive angles equal 180
- If a parallelogram has one right angle it has four right angles
What is special about the diagonals of a parallelogram?
They bisect each other and separate the parallelogram into two congruent triangles
What makes a quadrilateral a rectangle?
Opposite sides are parallel, opposite angles/sides are congruent, consecutive angles are equal to 180, diagonals bisect each other, all four angles equal to 90, diagonals are congruent
What makes a quadrilateral a rhombus?
Properties of parallelogram, diagonals are perpendicular, each diagonal bisects pair of opposite angles, diagonals are perpendicular.
What makes a quadrilateral a square?
If it has the properties of a rhombus and properties of a rectangle
What is a trapezoid?
One pair of parallel sides, also known as bases, and pair of nonparallel sides
What makes an isosceles trapezoid?
Non-parallel sides are congruent and base angles are congruent
What is the median do to a trapezoid?
The median is parallel to the bases.
How do you find the median of a trapezoid? How do you get rid of the fraction?
1/2(base1 + base2) multiply both ends by two
Recite the pythagorean theorem
the legs squared equal the hypotenuse squared
How to use the pythagorean theorem with altitude?
each leg a and b is geometric mean between hypotenuse c and the segment of the hypotenuse adjacent to that leg.
How to find hypotenuse in a 45-45-90 right triangle? How to find the leg?
H= L times square root of 2
L=1/2 H square root of 2
List the 7 properties of rectangles.
- opposite side are parallel/congruent. 2. Opposite angles are congruent 3. Consecutive angles are = 180
- all four angles are 90. 5. the diagonals bisect each other/ are congruent
How to find hypotenuse in a 30-60-90 triangle? The long leg? The short leg?
hypotenuse is twice the shorter leg. SL=1/2H
LL=1/2Hsqrt. of 3 Combine both: LL= SL sqrt. of 3
What make a parallelogram a rectangle?
the diagonals are congruent
Formula for sin ratio? R stands for the angle they give you.
leg opposite angle R/hypotenuse
formula for cos ratio?
leg adjacent/hypotenuse
When can you use trig ratios to find missing angles or sides in a right triangle?
if you have measures of 2 sides or if you know the measures of 1 side and an acute angle.
what is the law of sines?
sin A/a = sin B/b = sin C/c
formula for tan ratio?
leg opposite/leg adjacent
What is congruent in a rectangle?
the angles, the opposite sides, the diagonals
A parallelogram has one 90 degree angle. What can you expect of other angles?
the other three are 90
What are the properties of a rhombus?
properties of rectangle and parallelogram
What is special about the diagonals of a rhombus?
perpendicular
what is a trapezoid?
is a quadrilateral with exactly one pair of parallel sides
what are the bases in a trapezoid? The legs?
bases= parallel legs= nonparallel
what does a median separate the trapezoid into?
2 bases that are congruent
what makes an isosceles trapezoid?
if the legs are congruent
