VocabTheoremsPoints of Concurrency What’s Wrong? Solve It!Anything Goes… $ 100 $200 $300 $400 $500 J ΣθPARδY ! Mαth math Mαth JΣθPARδY! was created by GradeAmathhelp.com Mαth JΣθPARδY!

Vocab Three lines that intersect at the same point are _____________. Concurrent

Vocab The distance from a point to a line is measured using a ___________segment Perpendicular

Vocab How do you prove the midsegment DF is parallel to side AC? Parallel lines have the same slope

Vocab The __________ of a right triangle is always located across from the right angle. Hypotenuse

Vocab What do the circumcenter, the incenter, the centroid, and the orthocenter all have in common? They are all points of concurrency

Theorems 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 Which theorem is shown below? If m  ACP = m  PCB then, AP = PB Angle Bisector Theorem

Theorems What does the Concurrency of the Altitudes of a Triangle prove? Nothing (we only know the orthocenter)

Theorems 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 Perpendicular Bisectors of a triangle intersect at the ___________. Circumcenter

Points of Concurrency The Incenter is the point where _______ of a traingle intersect. Angle Bisectors

Points of Concurrency Which 2 points of concurrency are always found inside the triangle? Incenter & Centroid

Points of Concurrency Which Point of Concurrency is shown? Orthocenter

Points of Concurrency What is true about the points of concurrency of an isosceles triangle? They can be connected by the same line

What’s Wrong? The following diagram should show that D is on the angle bisector…. A C D B

What’s Wrong? A perpendicular bisector intersects a segment at the circumcenter of the segment. Circumcenter  midpoint

What’s Wrong? 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? 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? 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! Find x. x = 2

Solve It! What is the measure of OE if AE = 51? OE = 17

Solve It! Find the measure of BD BD = 61

Daily Double Find the distance of LZ LZ= √ 39

Solve It! Find the measure of LX LX = 12

Anything Goes… 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… In a Converse Theorem, what is true about the “if” and the “then” statements? The are switched

Anything Goes… 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… Find the perimeter of ∆ABC. Perimeter = 42

Anything Goes… If D is the midpoint of AB & E is the midpoint of AC, What is the distance of DE? 12.5