Geometry Exam

If it is an incenter, then it is formed by an?

Angle Bisector

What is this center?

Incenter

If it is an orthocenter, then it is formed by an?

Altitudes

What is this center?

Orthocenter

If it is a centroid, then it is formed by an?

Medians

What is this center ?

Centroid

If it is a circumcenter, then it is formed by an?

Perpendicular Bisectors

What is this center?

Circumcenter

What is a segment bisector?

A figure that cuts a segment into two equal parts (congruent segments).

What is a perpendicular bisector ?

a line that divides another line segment into two equal halves while intersecting it at a right angle (90^o)

What is an angle biscetor ?

a line that splits an angle into two equal angles.

90^o clockwise rotation rule” example: pre-image (x,y) “

after rotation (y,-x) turn the orderpair around and change the sign on the right

270^o counterclockwise rotation rule” example: pre-image (x,y) “

after rotation (y,-x) turn the orderpair around and change the sign on the right

90^o counterclockwise rotation rule” example: pre-image (x,y) “

after rotation (-y,x) turn the ordered pair around and change the sign on the left

270^o clockwise rotation rule” example: pre-image (x,y) “

after rotation (-y,x) turn the ordered pair around and change the sign on the left

180^o clockwise & counterclockwise rotation rule” example: pre-image (x,y) “

after rotation (-x,-y) keep the order pair the same just flip the signs )

y-axis reflcetion rule

flip the sign of the x-cordanant

x-axis reflection rule

flip the sign of the y-cordanant

What do you do if it ask you to move to the “right”

you add to the x cordanant

What do you do if it ask you to move to the “left”

you subtract from the x cordanant

What do you do if it ask you to move “up”

you add to the y cordinant

What do you do if it ask you to move “down”

you subtract from the y cordinant

What type of center triangle is this ? What is it formed by?

1)Circumcenter 2) perpendicular biscetor

What type of center triangle is this ? What is it formed by?

1)incenter 2) angle biscetor

For a triangle midsegment if you want to find “ line AB” what formula do you use ?

Big= 2 (little)

For an triangle midsegment If you want to find “angle ABC” what formula do you use ?

7x-45=-315 +4x (set them equal)

What is the distance formula ?

$$𝑑=\sqrt{(𝑥2-𝑥1)^2+\left(y2-y1\right)^2}$$

What is the slope formula

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

What pythagorean theorem formula is used to find a right triangle ?

$$c^2=a^2+b^2$$

What pythagorean theorem formula is used to find a acute triangle ?

c^2<a^2+b^2

What pythagorean theorem formula is used to find a obtuse triangle ?

c^2 > a^2 + b^2

What is the triangle inequality theorem ?

“Big” < or > Middle + Small

What analogy is used for “sin, cos ,tan” ?

$$SOME\frac{OLD}{HIPPIE}-CAUGHT\frac{ANOTHER}{HIPPIE}-TRIPPING\frac{ON}{ACID}$$

What makes a trapezoid?

At least one pair of parallel sides.

What makes a parallelogram?

Both pairs of opposite sides are parallel.

What makes a rhombus?

Four congruent sides.

What makes a rectangle?

4 right angles.

What makes a square?

4 congruent sides and 4 right angles

Altitude Theorem

$$\frac{SEG}{ALT}=\frac{ALT}{SEG}$$

Leg Theorum

$$\frac{HYP}{LEG}=\frac{LEG}{SEG}$$

What is this ? Congruent Yes or No ?

SSS Postulate and Yes

What is this ? Congruent Yes or No ?

SAS Postulate and Yes

What is this ? Congruent Yes or No ?

ASA Postulate and Yes

What is this ? Congruent Yes or No ?

AAS Theorum and No

What is this ? Congruent Yes or No ?

HL Theorum and Yes

To find a scale drawing the fomrula is ?

(drawing dimensions) (K) = (actual dimensions)

To find a scaled factor the formula is ?

(original diagonal)⋅k=(scaled diagonal)

What is NEW and OLD (The figure on the right is a scaled copy of the figure on the left)

Left = old

Right = new

How do identify the scale factor ?

$$\frac{new}{old}$$

If it told us A’ B’ and told us to find AB what would we do ?

Divide by the scale factor

If it told us AB and told us to find A’ B’ what would we do ?

Multiply by the scale factor

I will prove that triangle is right by demonstrating that

two of its sides are perpendicular to one another.

I will prove that triangle is isosceles right by demonstrating that

it has two sides that are of equal measure AND perpendicular.

I will prove that triangle is scalene by demonstrating that

it has three sides of unequal measure.

Which triangle has three sides of equal measure?

Equilateral triangle

I will prove that triangle is isosceles by demonstrating that

it has two sides of equal measure.