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Geometry
Math Chapter 6
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Terms in this set (25)
Name characteristics of a polygon.
- A closed figure made of segments
- No curves
- No sides cross
- Has to have three lines or more
Definition of convex.
No sides caving in.
Definition of concave.
A polygon where at least 2 sides cave in.
Definition of regular.
A polygon equilateral and equiangular.
Definition of equilateral.
All sides are equal or congruent
Definition of equiangular.
All angles are equal or congruent.
Name the polygon dependent upon the number of sides.
3 = triangle
4 = quadrilateral
5= pentagon
6 = hexagon
7 = heptagon
8 = octagon
9 = nonagon
10 = decagon
12 = dodecagon
Definition of parallelogram.
Quadrilateral with both pairs of opposite sides are parallel.
What are the four theorems of a parallelogram.
1. Opposite angles of a parallelogram are congruent
2. Opposite sides are congruent.
3. Each pair of consecutive angles are supplementary.
4. The diagonals of a parallelogram bisect each other.
Name the six theorems used in proving quadrilaterals parallelograms.
1. Prove that both pairs of opposite sides are parallel. (slope formula)
2. Prove that both pairs of opposite angles are congruent.
3. Prove that all pairs of consecutive angles are supplementary.
4. Prove that the diagonals bisect each other. (midpoint formula)
5. Prove that both pairs of opposite sides are congruent. (distance formula)
6. Prove that one pair of opposite sides are both congruent and parallel.
What is the rhombus rule?
A quadrilateral is a rhombus if and only if it has four congruent sides.
What is the rectangle rule?
A quadrilateral is a rectangle if and only if it has four right angles.
What is the square rule?
A quadrilateral is a square if and only if its a rhombus and a rectangle.
Name the two rhombus theorems.
1. If the diagonals of a parallelogram are perpendicular then it has to be a rhombus.
2. If each diagonal of a parallelogram bisects a pair of opposite angles then it is a rhombus.
What is the rectangle theorem?
If the diagonals of a parallelogram are congruent, then it is a rectangle.
What is a trapezoid?
A quadrilateral with only one pair of parallel sides.
What is an isosceles trapezoid?
A trapezoid with congruent legs.
Name the two isosceles trapezoid theorems.
1. The upper base angles are congruent and the lower base angles are congruent if the trapezoid is isosceles.
2. If the diagonals are congruent then the trapezoid is isosceles.
Rule for any trapezoid.
A pair of consecutive upper and lower base angles are always supplementary.
What is the midsegment of a trapezoid?
- A segment connects the midpoints of the legs.
- Parallel to the bases
- The average of the sum of the bases
What is a kite?
Two pairs of consecutive congruent sides, but opposite sides are not congruent.
Name the two kite theorems.
1. If a quadrilateral is a kite, then its diagonals are perpendicular.
2. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
Name the three ways of how to prove a quadrilateral is a rhombus.
1. Prove all four sides are congruent
2. Prove that it is a parallelogram first, then show the diagonals are perpendicular.
3. Prove that one pair of opposite angles have been bisected by the diagonal.
Remember to go over area formulas.
REMEMBER
Remember to go over the slope, midpoint, and distance formulas.
REMEMBER
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Verified questions
GEOMETRY
Two families set up tents at a state park. If the ranger's station located at (0, 0), and the locations of the tents are (0, 25) and (12, 9), write a coordinate proof to prove that the figure formed by the locations of the ranger's station and two tents is a right triangle.
GEOMETRY
Identify the hypothesis and conclusion of the conditional statement. If a convex polygon has five sides, then it is a pentagon.
GEOMETRY
A stop sign is a regular octagon. The signs are available in two sizes: 30 in. or 36 in. a. Find the area of a 30 m. sign. Round to the nearest tenth. b. Find the area of a 36 in. sign. Round to the nearest tenth. c. Find the percent increase in metal needed to make a 36 in. sign instead of a 30 in. sign.
GEOMETRY
A rancher wants to enclose a pen for new calves using 60 ft of fencing. Which shape uses all of the fencing and encloses the greatest area? F. a rectangle that is 12 ft by 18 feet G. a square 15 ft on each side H. a rectangle that is 20 ft by 30 feet I. a circle with an 8-ft radius