Geometry - Congruency (Part two)

What are vertical angles

Opposite angles that are equal, often across from eachother sharing the same vertex

What is a linear pair (also can be supplementary)

Angles that add up to 180, look for two angles next to each other that share a vertex and side and form a straight line

What are adjacent angles

Two angles that are next to each other

Whats a transveral

A line that crosses two or more lines

What is orientation

The direction a figure faces

What are complementary angles

Two angles thar add up to 90 degrees (have a right angle symbol)

What are alternate interior angles

Inside angles on opposite sides of a transversal

What are alternate exterior angles

Outside angles on opposite sides of the transversal

What are consecutive interior angles

Inside angles on the same side of a transversal

What are consecutive exterior angles

Outside angles on the same side of the transversal

What are corresponding angles

Angles in the same position at each intersection

How do you bisect an angle

1. Do a arch from one side of the angle to the other side

2. Put your bullseye on one point of the arch and make a line in the middle if the angle

3. Put your bullseye on the other point of the arch on the angle then make an intersecting line making a point appear

4. Connect the line to the angle

How do you find the number that an angle equals

Figure out the type of angle it is then decide if you either do 90 minus the reference angle or 180 minus the reference angle (or if its the same number as the reference angle)

What are the steps to doing a Translation of the segment AA’

1. Put your bullseye on A and measure to A’, make a mark

2. Don’t change the radius and move your bullseye to B then make a mark

3. Don’t change the radius and move your bullseye to C then make a mark

4. Measure from A to B then go to A’ and make an intersecting line for a point to go

5. Measure from A to C then go to A’ and make an intersecting line for a point to go

6. Then connect the points and your done

What are the steps of doing a Reflection over a line

1. Bullseye on A’

2. Slider/pencil tip little behind the line and draw a arch

3. On the arch you drew, wherever it intersects on the line of reflection you make a point

4. Put your bullseye on one of the points that intersected and draw a small arch, not changing the radius

5. Put your bullseye on the other intersecting point on the line of reflection then draw an arch again, not changing the radius

6. Make a point wherever the two new arch’s intersect, making A’’

7. Repeat these steps for B’’ and C’’

When doing a transformation, do you do the rotation about the origin first or do you do the reflection over the x-axis first?

Reflection over the x-axis first

1. Which way do you turn to do a Rotation of 90 degrees

2. Which way do you turn to do a Rotation of 180 degrees

3. Which way do you turn to do a Rotation of 270 degrees

4. Which way do you turn to do a Rotation of -90 degrees

1. Counter Clockwise once

2. Counter Clockwise twice (upside down)

3. Counter Clockwise three times

4. Clockwise once

If triangle ABC is mapped by a single isometric transformation to triangle A’B’C’, what isometric transformations could have preformed this?

Orientation is preserved so it is rotation or a translation.

Point A is mapped by a single isometric transformation to A’ such as A = A’. Name all the isometric transformations that could have preformed this

A reflection bc it has fixed points on the line of reflections, and a rotation bc the center point is fixed

Point B is reflected over segment GH resulting in G being the midpoint of segment BB’. What is the measure of angle BGH?

Measure angle BGH = 90 degrees bc reflections preserve distance and are done perpendicular to the line of reflection

How do you determine the missing values of an angle?

Do 180 minus the given number of one of the angles to find the other angle

Ex. If 46 was a number given on angle A and you had to find the number for angle B, you would do 180 minus 46 = 40 making 40 the missing number for B.

Mdpt formula

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

Distance formula

Square root

(x2 - x1) exponent 2 + (y2 - y1) exponent 2

Pythagorean theorem formula

a2 + b2 = c2