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Proofs

Help memorizing proofs

QuestionAnswer
A quad may be proved a parallelogram when 1. Both pairs of opposite sides are parallel. 2. Two opposite sides are both congruent and parallel. 3. Both pairs of opposite sides are congruent. 4. the diagonals bisect each other. 5. Both pairs of opposite angles are congruent.
To prove a quadrilateral is a rectangle, you can show 1. it is a parallelogram with congruent diagonals 2. it is a parallelogram with one right angle. 3. all four angles are right angles
To prove a quadrilateral is a rhombus, you can show: 1. it is a parallelogram with 2 consecutive sides congruent. 2. it has four congruent sides. 3. it is a parallelogram with perpendicular diagonals
To prove a quadrilateral is a square, you can show: 1. it is a rectangle with two consecutive sides congruent. 2. it is a rhombus with one right angle.
To prove you have a trapezoid: 1. You must use the slope formula to show one pair of opposite sides are parallel
To prove you have an isosceles trapezoid: 1. You must use the slope formula to show one pair of opposite sides are parallel AND the legs (the non-parallel sides) are congruent.
To prove you have a kite: 1. You must use the distance formula to show that two pairs of sides are congruent BUT not the opposite sides.
Steps of finding distance between a point and a line 1. Find slope and perpendicular slope. 2. Write the equation using point slope formula and the perpendicular slope. 3. Find the point of intersection by setting the two equations equal to each other. Plug x val into perp equation. Use distance form.
To determine the equation of a line of reflection (algebraically and graphically) 1. Midpoint of 4 points (2 points are the image and 2 are the og). 2. Find the slope of those midpoints. 3. Use point slope formula with any one of the two midpoints and the same slope to find the line equation.
Vertical line (x) undefined slope
horizontal (y) zero slope
Circumference 2nr
regular polygon formula 1/2 (perimeter)(apothem)
interior angle sum number of triangles x 180
1 interior angle interior angle sum / number of sides
exterior angle sum 360
1 exterior angle 360 / number of sides
area circle sector formula x / 360 nr^2
Created by: Rawesome
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