Common Reasons for Proofs
Congruence Statements
What congruence is missing?
Triangle Congruence
Triangle Congruence Postulates
Transformations
100
AB=AB
What is Reflexive Property?
100
Given this congruence statement, the angle congruent to angle V.
What is
angleH
100
1) When given parallel lines, we should look for congruent ______________________ angles.
2) If M is the midpoint of FD, what can we say is congruent?
1) Alternate Interior Angles are congruent.
2) FM = MD because M is exactly in the middle.
100
The congruence conjecture that proves these are congruent triangles.
What is SSS?
100
Are the following triangles congruent? If so, name the congruence postulates that proves it.
What is SSS?
100
P(4, -2) is translated 3 units left and 2 units down, then reflected over the x-axis. Find the coordinates of P'.
P'(1,4)
200
Given: AB||DE
What is the justification for this step:
∠BAC ≅ ∠EDC
What is Alternate Interior Angles are congruent when lines are parallel?
200
The side congruent to side VU
What is
bar{HI}
200
What congruent parts information would we need to know for the triangles to be congruent by ASA?
EC = DC
200
The congruence conjecture that proves these are congruent triangles.
What is SAS?
200
Are the following triangles congruent? If so, name the congruence postulates that proves it.
Not congruent
200
P(-3, 5) is reflected over the y-axis and then rotated 90° CCW. what are the coordinates of P'?
p'(-5, 3)
300
Given: C is the midpoint of AE.
The justification for this step:
bar{AC}congbar{CE}
What is Definition of midpoint?
300
A congruence statement for the two triangles represented by:
What is
triangleMNLcongtrianglePQR
300
What congruent parts would make these triangles congruent by AAS?
AC = DE
OR
BC = FE
300
Are the following triangles congruent? If so, name the congruence conjecture that proves it.
What is AAS?
300
Are the following triangles congruent? If so, name the congruence postulate that proves it.
Not congruent
300
Point A is in Quadrant II. Point A is first rotated 180°, reflected over the Y axis, and then translated left. What quadrant is Point A''' in?
Quadrant III
400
Given:
bar{AE} text( bisects )bar{BD}
The parts of the triangle that are now congruent:
What is
bar{BC} text( and )bar{CD}
400
The side congruent to IG
What is
bar{UW}
400
Which additional congruence given would allow these triangles to be congruent by ASA?
ASA if <F = <Q
400
Are the following triangles congruent? If so, name the congruence conjecture that proves it.
What is SAS?
400
Are the following triangles congruent? If so, name the congruence postulate that proves it.
What is HL?
400
First, reflect over the x-axis.
Second, Translate (x+3, y+1).
500
Given:
bar{BD} text( bisects )angleABC
Statement: (What parts of the triangle are now congruent: )
Reason:(What reason are these congruent?)
Statement:
angleABD text( = )angleCBD
Reason:
Definition of Angle Bisector
500
Congruence statement for the triangles represented by:
What is
triangleADBcongtriangleCEB
500
What additional information is necessary for the triangles to be congruent by SAS?
SAS if EG=RP
500
The additional information needed to prove the two triangles are congruent using HL theorem
What is Angle F = 90 degrees?
500
x = 5
y= 11
z = 7
500
Find the composition of two transformations that produces the image given the preimage below.
First, rotate 90° CCW.
Second, reflect over the x-axis.