Geo Chapter One

What is a point

An exact and single location

What is a line

An infinite and straight line made up of points

What is plane?

A flat surface that extends in all directions formed by 3 non-collinear points

What is a segment?

A portion of a line with a beginning and an end

What is a ray?

A portion of a line which extends in one direction

What is an angle?

The amount of turns between two rays that start at the same endpoint.

What is an acute angle?

An angle between 0° and 90°

What is an obtuse angle?

An angle greater than 90˚ and less than 180˚

What is a right angle?

A 90 degree angle

What is a straight angle?

A 180 degree angle

How do you find the restrictions of an angle?

1. Set up the limitations of the angle based on if it's obtuse or acute
2. Solve as usual (reduce and divide)

How do you find the length of a segment?

Subtract the two endpoints

What is a bisegment?

One point which bisects a line equally

What is a trisegment?

Two points which trisect a line equally

How do you find the coordinates of a point on a segment?

1. Find the segments (entire) length
2. Divide by number of points to find the length between each point
3. Start from one end and add

How do you find the degree of angle B from angle A?

1. Set up an equation based on what angle A is (acute/obtuse/right/straight), as angle C add up to angle A
1.2. [angle B + angle C = angle A's type]
2. Solve algebraically

What does the "ratio" of a measure mean?

Add an X

How do you find the measure of an angle A with congruent angle B?

1. They are equal, so set the equation up as so
2. Solve algebraically

How do you find a segment of a segment?

1. Similarly to an angle, find the measure of the (entire) segment, and set segment AB and segment BC equal to it
[segment AB + segment BC = segment AC]
2. Solve algebraically

How do you find the measure of segment AB with ratios and the measure of segment AC?

1. Set segment Ax + segment Bx to equal the measure of the overall segment
[segment ABx + segment BCx = segment AC's measure]
2. Find X algebraically
3. Use your solution to set the equation of segment AB
[AB(X) = measure of AB]

How do you find the measure of segment AB with the overall midpoint? (Given that both AB and BC are congruent)

1. Set segment AB and AC to equal each other
2. Solve for X and plug into segment AB

How do you find the measure of angle ABC with the bisection (line BD)?

1. Set angle ABD and angle DBC to equal each other
2. Solve for x
3. Set the same equation again, plugging in the value for X and solve

How do you justify your answer of a midpoint or bisection?

Solve for the overall measure