Vocab Theorems Points of Concurrenc

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What’s Wrong?

Solve It! Anything Goes…

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Vocab - 100

Three lines that intersect

at the same point are _____________.

Concurrent

Vocab - 200

The distance from a point

to a line is measured using a

___________segment

Perpendicular

Vocab - 300

How do you prove the midsegment DF is parallel to side AC?

Parallel lines have the same slope

Vocab - 400

The __________ of a right triangle is always located across from

the right angle.

Hypotenuse

Vocab - 500

What do the circumcenter, the incenter, the centroid, and the

orthocenter all have in common?

They are all points of concurrency

Theorems - 100

The Perpendicular Bisector theorem states:

If a point is on the perpendicular bisector of a segment, then __________________.

it is equidistant from the endpoints of the segment.

Daily Double

If you find the incenter of a triangle then, you know that which segments are congruent?

The perpendicular segments from the incenter to each side

Theorems - 300

Which theorem is shown below?

If mACP = mPCB

then, AP = PB

Angle Bisector Theorem

Theorems - 400

What does the Concurrency of the Altitudes of a Triangle prove?

Nothing (we only know the orthocenter)

Theorems - 500

State the Midsegment Theorem.

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

Points of Concurreny - 100

Perpendicular Bisectors of a triangle intersect at the

___________.

Circumcenter

Points of Concurrency - 200

The Incenter is the point where _______ of a traingle intersect.

Angle Bisectors

Points of Concurrency - 300

Which 2 points of concurrency are always found inside the triangle?

Incenter & Centroid

Points of Concurrency - 400

Which Point of Concurrency is shown?

Orthocenter

Points of Concurrency - 500

What is true about the points of concurrency of an

isosceles triangle?

They can be connected by the same line

What’s Wrong? - 100

The following diagram should show that D is on the angle bisector….

A

C

D

B

What’s Wrong? - 200

A perpendicular bisector intersects a segment at the

circumcenter of the segment.

What’s Wrong? - 300

What is wrong with this statement?

“The Point of Concurrency is the center of the

triangle.”Each of the four Points of Concurrency is in a different location in the triangle – not necessarily the “center”

What’s Wrong? - 400

What’s wrong with this statement?

“If you find the circumcenter, then you can prove the angle bisectors of the

triangle are congruent.” Cirumcenter proves the

segments from the circumcenter to the vertex are congruent

What’s Wrong? - 500

What’s wrong with this statement?

“If you find the centroid, then you know the length of the median of

the triangle.”

The centroid is 2/3 of the distance from the vertex to the opposite side.

Solve It! - 100

Find x.

x = 2

Solve It! - 200

What is the measure of OE if AE = 51?

OE = 17

Solve It! - 300

Find the measure of BD

BD = 61

Daily Double

Find the distance of LZ

LZ= √39

Solve It! - 500

Find the measure of LX

LX = 12

Anything Goes… - 100

Label the following information in the figure below…

A)C is a right angle

B)A B

C)AB = 8

D)AD bisects CB A B

D

C

A B

D

C

8

Anything Goes… - 200

In a Converse Theorem, what is true about the “if” and the “then” statements?

The are switched

Anything Goes… - 300

What is the difference between medians and altitudes

of a triangle?

Median: segment from a vertex to the midpoint of the opposite side.

Altitude: perpendicular segment from a vertex to the opposite side.

Anything Goes… - 400

Find the perimeter of ∆ABC.

Perimeter = 42

Anything Goes… - 500

If D is the midpoint of AB

& E is the midpoint of AC,

What is the distance of DE?

12.5