Modules 19-23 Flashcards
Complementary Angles
Angles that add up to 90 degrees
Supplementary
Angles that add up to 180 degrees
Vertical Angle Theorem
If two angles are vertical angles, then the angles are congruent
Perpendicular Bisector Theorem
If a point is perpendicular bisector, it’s equidistant from the endpoints of the segment
Equation for parallel line
Same slope. Input x and y into y=mx+b, solve for b.
Equation for perpendicular line
Slope is negative reciprocal. Input x and y into y=mx+b solve for b.
ASA Triangle Congruence
If two angles and included side is congruent to another triangle’s a, s, and a then triangles congruent.
SAS Triangle Congruence Theorem
If two sides and included angle is congruent to two sides and included angle of another triangle, then triangles congruent.
SSS Triangle Congruence Theorem
If 3 sides of a triangle congruent to 3 sides of another triangle, triangles are congruent.
AAS Congruence Theorem
If two angles and a non-included side of a triangle congruent to corresponding angle and non included side of another triangle, triangles congruent.
Distance Formula
√(x₂-x₁)²+(y₂-y₁)²
How to find sum of angles in a polygon?
n = sides, (n-2)180 degrees
Exterior Angle Theorem
Measure of an exterior angle of a triangle is equal to sum of measures of its remote interior angles
Isosceles Triangles
Triangle with two congruent sides
Triangle Inequality Theorem
Sum of any 2 lengths of triangle greater than third side length
How to find 3rd possible triangle side length?
Side 1 + x > Side 2
Side 2 + x > Side 1
Side 1 + Side 2 > x
Simplify
Circumcenter
center of circumcircle of a triangle. basically outside circle that touches all 3 vertices
How find circumcenter
Perpendicular bisector of side of a triangle intersect at point equidistant from vertices of the triangle.
Angle Bisector Theorem
If a point is on bisector of an angle, then its equidistant from the sides of the angle
Incircle
A circle inside a polygon that touches all sides of the polygon.
Median
Line where endpoint is vertex of triangle and opposite midpoint.
Centroid
Intersection of 3 medians
Centroid Theorem
centroid of a triangle is 2/3 the distance from vertex to midpoint of opposite side
Midpoint Formula
((x1+x2)/2, (y1+y2)/2))
Altitude
Perpendicular segment from a vertex to line on opposite side
Orthocenter
Point where altitudes intersect
Location of orthocenter depending on type of triangle
Acute: Inside triangle
Obtuse: Outside triangle
Right: Lies on vertex of right angle
Find orthocenter with coordinates?
Find perpendicular slope equation of one side. Use point-slope form insert vertex coord, do for 2 sides.
midsegment
line segment that connects 2 midpoints of a triangle. Is 1/2 the length of the parallel line.
HL Triangle Congruence Theorem
If the hypotenuse and leg of a right triangle is congruent to corresponding hypo+leg, right triangles are congruent.
Centroid with coordinations
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
