Name the Theorem
Triangle Congruence
Triangle Properties
Points of Concurrency
Proofs
100
You want to find the value of x and the measure of angles J, H, & S. What theorem can be used to solve this problem? Give the name and description of the theorem.
Triangle sum theorem: The sum of all the angles in the triangle is 180 degrees.
100
Which of the following is NOT a congruence postulate:
AAS
ASA
SSS
SSA
HL
SAS
AAA
SSA & AAA
100
In the diagram below, DE = 12, EF = 18, and FC = 9. What is the length of BC?
6
100
What type of segments are DG, EG, and FG?
perpendicular bisectors
100
What is the reason for statement 2?
Definition of angle bisector
200
ED=22 but you want to know the length of BC. What theorem can be used to solve this problem? Give the name and description of the theorem.
Midsegment theorem: The midsegment is half the length of the side it is parallel to.
200
ΔABC ≅ ΔDEF. Which angle and side from ΔDEF correspond with ∠ B and segment CA?
∠ B ≅ ___
CA ≅ ___
∠ E & segment FD
200
You are on a boat x distance away from the Statue of Liberty. Compare the length of x to 305ft.
X ___ 305ft
x>305 ft
200
Point G is what point of concurrency?
Incenter
200
What is the reason for statement 3?
reflexive property
300
You want to know if x if greater than 200ft. What theorem can be used to solve this problem? Give the name and description of the theorem.
Hinge theorem: The side across from the larger angle is longer.
300
Name the transformation and congruence postulate:
Rotation & SAS
300
Write an equation that can be used to find the value of x.
11x+6+4x+9x+6=180
300
G is the circumcenter in triangle ABC. Write an equation that could be used to find the value of x.
6x-15=4x+7
300
Write a congruence statement for the triangles. (statement 4)
ΔFGH ≅ _____
ΔFGH ≅ ΔFIH
400
You want to find a range of possible lengths for DB. What theorem can be used to solve this problem? Give the name and description of the theorem.
Triangle inequality theorem: The sum of two sides of a triangle must be greater than the third side.
400
A translation followed by a rotation about point D shows that ΔABC ≅ ΔDEF. Give the degree of counterclockwise rotation that must be done to ΔDEF.
270 degrees
400
ΔABC is shown. D is a point on AB, AC=8, BC=19, and AD=7. Which could be a length of DB?
4, 13, 20, or 27
13
400
In ΔABC, AD, BE, and CF are the medians of the triangle. Write an equation that can be used to find the value of x.
2(2x+2)=7x-5
400
What congruence postulate can be stated for reason 4?
AAS
500
You want to find the value of y and the measure of angles A & B. What theorem can be used to solve this problem? Give the name and description of the theorem.
Exterior angles theorem: The exterior angle equals the sum of the two remote interior angles.
500
A translation followed by a rotation about point D shows that ΔABC ≅ ΔDEF. Give the algebraic description of the translation that maps point D onto it's corresponding point.
(x,y)->(x+2,y-2)
500
What is the value of x and the length of FG?
x=7
FG=17
500
Find the length of BE.
24
500
What is reason 5?
CPCTC