Download n is the # of sides

Part 2
Unit 4-Review
Part 2- Segment in a triangle
Name of relationship
In words/ Symbols
360
1. Exterior angles in a polygon.
a). ONE Exterior
b) Sum of Exterior
and Angle Relationships
a)
𝑛
n is the # of sides
b) Sum of Interior.
3. Segments in a triangle:
Exterior angles and formed by
extending a side of the triangle.
b) Sum is AlWAYS 360 degrees( NO MATH
NEEDED)
2. Interior angles in a polygon.
a) ONE Interior
Diagrams/ Hints/ Techniques
a) The supplement of on Exterior angle-they are
linear pairs!--> Exterior + Interior = 180
Remember! One exterior and one interior angle
add up to 180 degrees!
b) Number of △ ′𝑠 times 180.  ( n-2)180
Medians- Goes to the midpoint of the opposite side
creating two equal segments
Altitudes-Are perpendicular to the opposite side
creating right angles
Perpendicular bisectors- Goes to the midpoint of
opposite side and is perpendicular to it.
Angle bisectors- bisects the angle at the vertex it
goes through making 2 congruent angles.
** In Isosceles and Equilateral triangles these
segments coincide!
4. Points of concurrence.
Angle
Bisector
⊥
Bisector
2 or more medians Centroid : Always inside the
triangle. Cuts each median into a 2:1 ratio
2 or more Altitudes Orthocenter: Inside for acute
triangles, on the triangle for right triangles and
outside for obtuse triangles.
2 or more angle bisectors Incenter: Always inside
the triangle.
ALL OF MY CHILDREN ARE
BRING IN PEANUT BUTTER
COOKIES.
2 or more perpendicular bisectors Circumcenter:
Inside for acute triangles, on the triangle for right
triangles and outside for obtuse triangles.
5.Centroid and Ratios
Centroid cuts every median into a 2:1 ratio. Use this
ratio to set up equation 2X + 1x= whole length of
median.
Read carefully- What is the segment they want?
Sometimes you need to substitute back in!
Part 2
1) In the diagram below of quadrilateral ABCD with diagonal
, and
. If
is parallel to
,
,
,
, find m < 𝐴𝐵𝐷
2) Using the inferences provided, identify each of the segments as one of the following for
Δ𝐶𝐵𝐴:
Altitude, Median, angle bisector, or perpendicular bisector.
B
̅̅̅̅
̅̅̅̅ ⊥ 𝐴𝐶
a. Given: 𝐵𝐷
̅̅̅̅
𝐵𝐷 must be a(n)
G
A
̅̅̅̅
b. Given: ̅̅̅̅
𝐴𝐸 ≅ 𝐸𝐶
̅̅̅̅
𝐵𝐸 must be a(n)
c. Given: ∡𝐴𝐵𝐹 ≅ ∡𝐶𝐵𝐹
̅̅̅̅ must be a(n)
𝐵𝐹
d. Given ̅̅̅̅
𝐺𝐸 ⊥ ̅̅̅̅
𝐴𝐶 𝑎𝑛𝑑 ̅̅̅̅
𝐴𝐸 ≅ ̅̅̅̅
𝐸𝐶
̅̅̅̅ must be a(n)
𝐺𝐸
E
C
F
D
Part 2
3) Adrian thinks the segment NK in the following triangle is an altitude while Daniel thinks
it’s a median. Is Adrian correct? IS Daniel correct? Are they both correct? Are they both
incorrect? EXPLAIN!
4)
Find the coordinates of the centroid of the triangle with the given vertices.
J(−1, 2), K(5, 6), L(5, −2)
5) Find one of the exterior angles of a regular decagon.
6) Find the measure of one interior angle of a regular nonagon (9 sides).
7) Find the number of sides of a polygon whose sum of interior angles in 1620°.
Part 2
8) a. Circle the point of concurrence that is formed when 2 or more altitudes intersect.
Centroid
Orthocenter
Incenter
Circumcenter
e. Where could this point be located? ( circle all that apply)
Inside the triangle
outside the triangle
On the triangle
9) a. Circle the point of concurrence that is formed when 2 or more medians intersect.
Centroid
Orthocenter
Incenter
Circumcenter
f.
Where could this point be located? ( circle all that apply)
Inside the triangle
outside the triangle
On the triangle
10) In triangle ABC, ̅̅̅̅̅
𝐴𝐷, ̅̅̅̅̅
𝐶𝐹, and ̅̅̅̅
𝐵𝐸 are medians. If ̅̅̅̅
𝐶𝐹 = 33, find CG and FG.
In ∆𝐷𝐸𝐹, 𝑚∠𝐷 = 3𝑥 + 5, 𝑚∠𝐸 = 4𝑥 − 15, 𝑎𝑛𝑑 𝑚∠𝐹 = 2𝑥 + 10. Which statement would be true?