Download SKILL #1 NON-NEGOTIABLE SKILL #1 The diagram below shows a

SKILL #1
NON-NEGOTIABLE SKILL #1
The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each
measure 13, the altitude is x, and the base is 10. Find the length of the altitude.
10
SKILL #2
NON-NEGOTIABLE SKILL #2
In the diagram below,
What is
and
?
are shown with
and
.
SKILL #3
NON-NEGOTIABLE SKILL #3
What is the measure of an interior angle of a regular octagon?
What is the sum of the interior angles of the same octagon?
SKILL #4
NON-NEGOTIABLE SKILL #4
In triangle ADC, Segment DE is the altitude of the triangle. AE = 5x EC= 4x +3 and
m∡ 𝐷𝐸𝐴 = 5x +5. Solve for x.
Name: _____________ Station 1: Angle Side Relationships and Triangle inequality Theorem
Geometry Pd. ______
1) In triangle RQS, RQ= 10 inches, SQ =9 inches and RS= 8 inches, arrange the angles form smallest
to greatest.
2) The diagram at the right shows a right triangle with representations for two angles. What is the
value of x?
3) In triangle DOG, m∡D = 400 , m∡O= 600 ,, and m∡G = 800 ,.
State the longest side of the triangle __________________
State the shortest side of the triangle _________________
Classify the triangle based on its SIDES ___________________
4) State whether each of the following could be the sides of a triangle and why.
a) {6,6,6}
b) {2,2,4}
c) {5,9,10}
d) {4,4,9}
5) Two sides of a triangle have lengths 2 and 7. Write an inequality for all possible integer lengths
of the third side.
6) In the diagram below of quadrilateral ABCD with diagonal
, and
. If
is parallel to
,
,
, find m < 𝐴𝐵𝐷
,
Name: _____
Geometry Pd. ____
1)
Station 2: Pythagorean, Isosceles Triangle and Exterior angle Theorems
Given the following information find the degrees in each angle of the triangle.
<ABC = ________________
<BCA = ________________
<BAC = _______________
What is the longest side of the triangle? ___________________________
2) Determine whether the following sides form a right , acute or obtuse triangle. Justify your answer
with words.
a) 5, 11, 12
3)
b) 5, 12, 13
c) 7, 15, 18
4) Solve for x . Give your
answer in the simplest radical form.
5) In the diagram below of DBCD , side DB is extended to point A.
(Note: The diagram above is not drawn to scale)
Which statement must be true?
(1) mÐC > mÐD
(2) mABC  mD
(3) mÐABC > mÐC
(4) mÐABC > mÐC + mÐD
6) In a triangle, the ratio of the angles is 1:3:5. Find the measure of all the angles and Classify the
triangle according to its angles.
Name: ________
Station 3: Points of concurrency and Exterior/Interior angles in polygons.
Geometry Pd. ______
1) Using the inferences provided, identify each of the segments as one of the following for
Δ𝐶𝐵𝐴:
Altitude, Median, angle bisector, or perpendicular bisector.
B
a. Given: ̅̅̅̅
𝐵𝐷 ⊥ ̅̅̅̅
𝐴𝐶
̅̅̅̅ must be a(n)
𝐵𝐷
G
A
b. Given: ̅̅̅̅
𝐴𝐸 ≅ ̅̅̅̅
𝐸𝐶
̅̅̅̅ must be a(n)
𝐵𝐸
c. Given: ∡𝐴𝐵𝐹 ≅ ∡𝐶𝐵𝐹
̅̅̅̅
𝐵𝐹 must be a(n)
E
F
D
C
̅̅̅̅ ⊥ 𝐴𝐶
̅̅̅̅ 𝑎𝑛𝑑 ̅̅̅̅
̅̅̅̅
d. Given 𝐺𝐸
𝐴𝐸 ≅ 𝐸𝐶
̅̅̅̅
𝐺𝐸 must be a(n)
2) 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!
3)
Find the coordinates of the centroid of the triangle with the given vertices.
J(−1, 2), K(5, 6), L(5, −2)
4) Find one of the exterior angles of a regular decagon.
5) Find the measure of one interior angle of a regular nonagon (9 sides).
6) Find the number of sides of a polygon whose sum of interior angles in 1620°.
7) a. Circle the point of concurrence that is formed when 2 or more altitudes intersect.
Centroid
Orthocenter
Incenter
Circumcenter
a. Where could this point be located? ( circle all that apply)
Inside the triangle
outside the triangle
8)
On the triangle
a. Circle the point of concurrence that is formed when 2 or more medians intersect.
Centroid
Orthocenter
Incenter
Circumcenter
a. Where could this point be located? ( circle all that apply)
Inside the triangle
outside the triangle
On the triangle
̅̅̅̅̅ and ̅̅̅̅
9) In triangle ABC, ̅̅̅̅̅
𝐴𝐷, 𝐶𝐹,
𝐵𝐸 are medians. If ̅̅̅̅
𝐶𝐹 = 33, find CG and FG.