Modules 19-23

Question 1

Complementary Angles

Answer 1

Angles that add up to 90 degrees

Question 2

Supplementary

Answer 2

Angles that add up to 180 degrees

Question 3

Vertical Angle Theorem

Answer 3

If two angles are vertical angles, then the angles are congruent

Question 4

Perpendicular Bisector Theorem

Answer 4

If a point is perpendicular bisector, it’s equidistant from the endpoints of the segment

Question 5

Equation for parallel line

Answer 5

Same slope. Input x and y into y=mx+b, solve for b.

Question 6

Equation for perpendicular line

Answer 6

Slope is negative reciprocal. Input x and y into y=mx+b solve for b.

Question 7

ASA Triangle Congruence

Answer 7

If two angles and included side is congruent to another triangle’s a, s, and a then triangles congruent.

Question 8

SAS Triangle Congruence Theorem

Answer 8

If two sides and included angle is congruent to two sides and included angle of another triangle, then triangles congruent.

Question 9

SSS Triangle Congruence Theorem

Answer 9

If 3 sides of a triangle congruent to 3 sides of another triangle, triangles are congruent.

Question 10

AAS Congruence Theorem

Answer 10

If two angles and a non-included side of a triangle congruent to corresponding angle and non included side of another triangle, triangles congruent.

Question 11

Distance Formula

Answer 11

√(x₂-x₁)²+(y₂-y₁)²

Question 12

How to find sum of angles in a polygon?

Answer 12

n = sides, (n-2)180 degrees

Question 13

Exterior Angle Theorem

Answer 13

Measure of an exterior angle of a triangle is equal to sum of measures of its remote interior angles

Question 14

Isosceles Triangles

Answer 14

Triangle with two congruent sides

Question 15

Triangle Inequality Theorem

Answer 15

Sum of any 2 lengths of triangle greater than third side length

Question 16

How to find 3rd possible triangle side length?

Answer 16

Side 1 + x > Side 2
Side 2 + x > Side 1
Side 1 + Side 2 > x
Simplify

Question 17

Circumcenter

Answer 17

center of circumcircle of a triangle. basically outside circle that touches all 3 vertices

Question 18

How find circumcenter

Answer 18

Perpendicular bisector of side of a triangle intersect at point equidistant from vertices of the triangle.

Question 19

Angle Bisector Theorem

Answer 19

If a point is on bisector of an angle, then its equidistant from the sides of the angle

Question 20

Incircle

Answer 20

A circle inside a polygon that touches all sides of the polygon.

Question 21

Median

Answer 21

Line where endpoint is vertex of triangle and opposite midpoint.

Question 22

Centroid

Answer 22

Intersection of 3 medians

Question 23

Centroid Theorem

Answer 23

centroid of a triangle is 2/3 the distance from vertex to midpoint of opposite side

Question 24

Midpoint Formula

Answer 24

((x1+x2)/2, (y1+y2)/2))

Question 25

Altitude

Answer 25

Perpendicular segment from a vertex to line on opposite side

Question 26

Orthocenter

Answer 26

Point where altitudes intersect

Question 27

Location of orthocenter depending on type of triangle

Answer 27

Acute: Inside triangle Obtuse: Outside triangle Right: Lies on vertex of right angle

Question 28

Find orthocenter with coordinates?

Answer 28

Find perpendicular slope equation of one side. Use point-slope form insert vertex coord, do for 2 sides.

Question 29

midsegment

Answer 29

line segment that connects 2 midpoints of a triangle. Is 1/2 the length of the parallel line.

Question 30

HL Triangle Congruence Theorem

Answer 30

If the hypotenuse and leg of a right triangle is congruent to corresponding hypo+leg, right triangles are congruent.

Question 31

Centroid with coordinations

Answer 31

((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)